First I know you put plenty of effort into this, but let us make no unproven assumptions. I think part of your problem is that you have over-complicated the problem.
What Do We Desire?
Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise.
This is the closure reason we usually apply when we suspect an answer can not be adequately corroborated. Sometimes, it seems to me as if Primarily Opinion Based is misread, as if it was just "Opinion Based" but I do not believe that is the case. As you can see, from the closure reason itself, there is some amount of leeway, for "some degree of opinion".
If you can base your answer in "facts, references or specific expertise" for us to serve as a basis for our votes, then we welcome it to be audited by our system of peer review. What we generally try to avoid is answers that are merely "based almost entirely on opinion." The definitive post for what constitutes a Primarily Opinion Based question on the Stack Exchange network is Good Subjective, Bad Subjective.. In my opinion, the standards are not especially high, and I think we can even go all the way down to anecdotal evidence based on the moms4moms example, provided that the anecdote is sufficiently explanatory and relevant.
What we dislike is for people to just claim "There is no such word!" and without any further reason to believe them. That is just an opinion that does nothing to settle anybody's doubt, since there is a high likelihood that it may very well be wrong. According to Improve Your Speed Reading by Phil Heartman, a joint Google/Harvard study revealed approximately one million words in the language, and the adult only vocabulary ranges between 35,000–75,000, which only represents about 5% of the typical vocabulary in Phil's approximation. Just to stress how good of a vocabulary 75,000 words is, Noah Webster's magnum opus, An American Dictionary of the English Language contained approximately 70,000 words upon its first publication in 1828. It took him 26 years to complete, and was the largest dictionary available of its time. I doubt that anybody else is as renowned for mastery of the English Language vocabulary as him, as his surname has become something of an eponym for the very concept of a dictionary in the U.S.A.
This is one of my principle interests in single-word-requests, because the Stack Exchange system can be exceptionally good at sussing out especially rare words by crowd-sourcing information.
This is not to say that "no such word exists" is never a good answer. The community has already established that "no such word exists" is a perfectly valid answer to single word requests in these questions:
I am not against people doing that if they want to do so. It seems like the best solution to the problem, if somebody is willing to do it properly. However, I do not think we should be suspending our normal expectations of what constitutes a good answer.
So How Can We Answer Questions Regarding Nonexistence Well?
Although I do not want to foreclose upon any good methods of doing it, I believe a principle concern in this question is how to corraborate the answer. The way I see it, there are at least a few ways:
Specific Expertise
Some people need certain kinds of words more than others, and are hence more likely to know if a word within a certain category exists than other people, so one way to answer is for such a person to claim no such word exists. This seems to be the approach Professor John Lawler took to answering
Is There One Term for Grammar, Punctuation and Spelling? Now, I somewhat disagree with the answer and hope to eventually write my own answer arguing that grammar is the best word based on historical usage, and my own interest in the subject matter of what grammar means is why I know of this question in the first place.
Nevertheless I still think it serves as a good example of the sort of value that type of answer may have especially since Prof. Lawler is a very well respected expert within our community, and it probably still goes to show that the existence of another such word within the scholarly community is quite unlikely, since it would not be so troublesome for him to suggest it if he had ever heard of one, and I think most of us can agree it would probably be him if anybody had ever heard of such a word.
References
Another way to show that something does not exist is to show that it is not where anybody would expect it to be if it did exist. This is similar to the tactic of looking through the closet and shining a light under the bed to assure to frightened children who do not know any better that the boogeyman is not going to eat them as soon as they are tucked under the covers and close their eyes.
This is part of the approach I took with Are The “Paraphrase Brackets” (Not Square Brackets) Used in English? With all of the evidence I provided that such a thing is unlikely to exist in our language, my answer received seven votes for it, as opposed to the three Hotlicks received for posting the same conclusion without any evidence at all. Hotlicks has more reputation points than me, and posted his answer earlier too, so it is out of appreciation for my evidence that my answer outshone his. You and Guildenstem even honored me by providing some direct approbation for my research:
The bit about the Manding languages was really intriguing. I wondered if these languages needed paraphrase brackets because paraphrasing is an important or fundamental part of their discourse (relatively more than other languages, I mean). The question occurred to me because I know there are some languages, like Pirahã, which inflect for the "source of knowledge" (1st hand, 2nd hand, etc), which would be more important in oral-only communities. Sadly I didn't find anything interesting on a quick search, though Wikipedia does mention these communities have "a strong oral tradition.—Dan Bron
What an exceptionally thorough and well-researched answer.—Guildenstern
Now this is much more difficult with words than a proper dictionary, since there are so many more of them. However, the place you would expect to usually find those are dictionaries.
Nevertheless, despite however difficult proving an absence may be using this method, it is still hypothetically possible. As incredible as it may seem, there is at least one person out there who have read the entire 20 volume Oxford English Dictionary second edition. Ammon Shea undertook the task by reading eight hours a day for a year, documented the experience in a book entitled Reading the OED: One Man, One Year, 21,730 Pages. He was interviewed by reputable news outlets like N.P.R. and the British Broadcasting Corporation.
Additionally, this does not have to be a full time job: Despite however many volumes it has, the latest print edition of the Oxford English Dictionary is not an especially word entry dense publication with its 218,632 total words (its many pages mostly contain examples of historical use, with many extra definitions). I think it might be realistic for us to read at least a single volume of an unabridged dictionary. Those advertise word totals ranging from 315,000 like the Random House Webster's Unabridged Dictionary, Second Edition, to 700,000 words like Collins English Dictionary—Complete and Unabridged. The Oxford Dictionaries Blog claims that the task of reading the Oxford Dictionary of English only takes 41 hours of continuous reading.
I admit, that is plenty of work, but some people have done it with no real end goal in sight, and if somebody wanted to undertake the task, the result could be widely applicable to the range of word request questions on our site, and constitute a form of expertise that would be unwise to turn away. I have also noticed that people have undertaken the task of reading the whole Oxford Canadian Dictionary, such as Nikki Love (A, B, C, D-H, I-O, P-S, T-Z). Additionally, the use of specialty dictionaries can help to lessen the task or find especially arcane words.
Now the issue of trust has been raised, and I do agree that this is a somewhat legitimate source of concern, since anybody can claim they did something when they did not, but usually, when somebody discloses their credentials, such as being a native speaker of a certain dialect or a professional linguist, we give them the benefit of our trust. I don't see why "I read an entire dictionary" should be much different, especially since a skeptic can audit the claim by another reading of the same dictionary. At any rate, if we should verify what a person's credentials are and how we should go about it, is a problem that should be considered separately, in my opinion.
Explaining the Facts
Sometimes a word is more likely to exist than not simply due to the facts surrounding it, and providing a good explanation may just be able to prove that. It may require the use of some creative logic.
In order to exemplify some of what I mean, I submit some answers which I wrote that which take novel approaches with etymology to trying and disprove the existence of a word:
You should recognize my etymologically based attempt to disprove the existence of the word lexophillia. Granted, this is not a single-word-request but perhaps similar guidance regarding how to disprove the existence of the word can be taken from other is-it-a-word questions.
More directly applicable is in Is *There a Word Analogous to “Dual” for Three or More Options?, I try to select and dismiss the closest possible match to the question * I claim that if there was to be a word within that series, that it must be trial, and then I show how trial is not the word.
Propose Alternative Solutions Instead
Sometimes even a good question does not have a good direct answer, but if a question such as the one described is asked well enough, we can explain what the next best alternative is. Although I believe I have adequately demonstrated that there is no perfectly analogous word to the word dual, the other members have tried to suggest would-be synonyms which would match the given context. The accepted answer is Triple, and the top voted answer is Threefold. Stack Exchange encourages this in How Do I Write A Good Answer.
Indeed, if the questioner describes what it is they want well enough an alternative answer may even invoke serendipity:
The Happy faculty, or luck, of finding, by "accidental sagacity," interesting items of information or unexpected proofs of one's theories; discovery of things unsought: A factitious word humorously invented by Horace Walpole.[—The Century Dictionary and Cyclopedia Supplement]
Combining Solutions
Although implementing just any one of these solutions should be good enough if done well, there is no need to restrict yourself to implementing just one. Some of these work especially well in combination. For instance, reading an entire dictionary may just give you a sense of how people would communicate the desired concept, if no match for the precise concept exists, and so you can comprehensively document which alternatives you have encountered that seem best to better prove you have undertaken the task.
Addressing the Methods of Dealing with the Problem
Preferably speaking, I would prefer for solution 1 to be implemented, if somebody is willing to do it properly. By using the aforementioned techniques, we can actually learn something about the language. If somebody wants to try, I see no really good reason to stop them.
However, in implementing the first solution, we have to acknowledge that solution no. 2 may be the one that is implemented most often in practice, because this is a volunteer run website. Sometimes people just are not going to want to answer a question, especially if it is an odd and relatively insignificant request. As long as a question remains open, it is up to the people who consider answering to decide whether or not they want to try.
A Solution I Think We Should Avoid
In a case such as the one you describe, this option is not one that I would like us to implement this possible solution to the problem:
- The question is closed because there can never be an actual “answer”, so it is barred from receiving non-answers.
I do not see much merit in this approach to the problem over just ignoring the question. The only benefit I see in it over ignoring the question is that it forecloses upon wrong answers, but some wrong answers, and other qualitatively bad answers, are supposed to be on the website for the sake of giving meaning to our system of peer review. That is why Stack Exchange allows voting against answers, unlike hackernews. If adequate evidence to the contrary is provided, then we can just let votes sort out any incorrect claims to the contrary.
We do not want to be answering meaningless questions like questions like What's Your Favorite Word that other Q & A. websites without our policies like Yahoo Answers or Quora gets, where all answers are equally correct, without any need for explanation. The relevant closure reason has been quite good at keeping our website neat and tidy. It may just be that English Language & Usage never got such a question because this type of problem was spotted early on Stack Overflow, or perhaps all such questions have been deleted, but we do not receive that type of question here.
Another more commonly applicable purpose for this closure reason is naming questions, on the grounds that a proper noun could hypothetically borrow from any word, or be created from scratch to address this issue. Whatever these, and other Primarily Opinion Based questions may have, they do not exist for the sake of the pursuit of truth, and may even obstruct it, so Stack Exchange as a whole has decided to eschew them. I have seen these are expressly singled out in our help center.
However, when I cite those standards, it needs to be remembered that too much closure can be an obstruction to the pursuit of truth too, since the main purpose of it is to preclude all answers to a problematic question. This includes any potential good answers.
The over-application of closure has been a problem for the Stack Exchange network in the past. Stack Exchange noted that also rejected a more specific "too narrow" closure reason to replace it, on the grounds that it is very hard to objectively determine just what people need. Similarly, the closure system as a whole was reworked in 2013 in part to clarify the reasons for closure, and in part to restrain them. As an example of such restraint, The Too Localized closure reason was long, confusing and over-applied, and the Stack Exchange network has recanted upon it, and even rejected a network-wide 'too narrow' closure reason as still being too much. Similarly, we used to have a Not Constructive closure reason:
As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or specific expertise, but this question will likely solicit debate, arguments, polling, or extended discussion.
This has been reworked into Primarily Opinion Based, which is somewhat more permissive:
Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise.
If we took the closure approach of trying to answer questions like this, I might not have had the chance to post my answer to What Is A Noun For Something That Edifies Us during the few days while I was waiting for the questioner to fulfill my request divulge research. In the meantime, somebody suggested no such word exists, and proposed using an "adjective" instead of a noun. With a little bit of luck, and a somewhat novel approach, I did very easily find a word that almost no current dictionary contains, with the exceptions being Merriam-Webster's New International Dictionary, Third Edition, and its online counterpart. I also almost certainly would not have had the chance to answer the aforementioned paraphrase bracket question which went unanswered for a period from November of 2016 to march of 2017.
Also worthy of note is that question closure is "supposed to be a (mostly) spontaneous action", so if the community achieves a consensus on a certain point of policy, then it is possible that other positive contributions I have mentioned could be swiftly blocked by a few people who overestimate the worth of their independent vocabulary.
Sometimes good things come to those who wait, and I do not think we should be so fearful of a question that is not being answered anyway that we should foreclose upon it being answered entirely. Denying other people the opportunity to report if they have discovered such a thing does little to reassure people that no such thing exists. It is fine for hypothetically answerable questions to wait for an answer. That is why the unanswered questions tab exists.. In a case like this, I see no benefit over solution number 3 (closure) over solution number 2 (just ignore it). I think it is needless to prevent answers to a question if nobody is answering it anyway.
Finally, I think it is also worth noting that we already close most of the questions we receive. I have seen numbers reported as high as 60%. Can we please us not grow even more trigger happy with the closure button than we already are, and lose decent contributions in the process: Please? Pretty please? I'll put sugar on top if I must!