Here are some thoughts I have on the matter:
The probable reason
One thing that needs to be considered is that it takes time for things to be processed through the review queue, and even if a question is rendered acceptable by community standards, there is no guarantee that it will get enough exposure. That the questions were reopened here at meta suggests to me that this was probably why it remained closed after your edit.
Some Other Reasons for Concern
I agree that there are conflicting ideologies regarding the research guidance. It seems to be roughly down the middle between the philosophy of General Reference Standard wherein a commonly available resource that adequately answers the question needs to actually exist for a question to be closed, and Show the Research Standard where any question which fails to produce research is closed. Each proceedure has its own pros and cons. However, it should first be noted that they both share the same common motivations of addressing overly simple questions, and even some of the same outcomes.
Regarding those common outcomes
I think that we can rule out the Oxford English Dictionary as being the reason for closure. In the first case, questions are given impunity from a research requirement when a direct authoritative answer is not readily available to the general public, and even when the O.E.D. does authoritatively answer a question, its text is not made readily available. In the latter case, we presume that the questioner's own research efforts are enough to prove that just any ol' answer is not enough, almost irrespective of what resources they choose for their research. Either way, lack of accessibility is not a concern here.
Regarding those common motivations
Those are mostly explained in Are Some Questions Too Simple by Jeff Atwood, and the question Should We Introduce A Reasonable Research Standard. We are trying to prevent questions that can be can be "definitively and permanently answered by a single link to a standard internet reference site "with no additional explanation necessary." and to "draw the line in order to avoid English Language & Usage becoming an aggregator of other online resources".
Specific Thoughts Regarding Case 1
I am concerned about the outcome of this case. My own cursory research, to determine if the question complies with the general reference flowchart, was to check to see what the search results for "On the Nose" and Origin was on google, duckduckgo and bing (which won't archive unfortunately). In all three cases I got the phrasefinder's answer within the first three results. It was the top answer on Bing and Google. In this respect, your edit in the first case failed to serve the purpose of our closure reason. I believe that these are reasonably obvious search terms, and if I am not mistaken in that respect, any question regarding this subject should include that article in its research and explain why it is suspected to be inadequate, because it is the first place any reasonable effort would have looked. Just to be clear, I do not mean to suggest that anything that can be found with the aid of a search engine should be barred, but it should not be from a trusted resource within the first few results of the most cursory search for the subject.
You did not want to do that, because you thought it would be overly transformative and put words in the questioner's mouth. I do respect that, because that has its own problems, and as such would be against editing guidelines that prohibit changing the intention of the post. If I recall correctly, one of the reasons an edit can be rejected in the review queue is because it attempts to answer the question, which is effectively what adding research often seems like it tries to do.
However, as a result, the phrasefinder's answer was also included in an answer that simply aggregated theories with no further user input, which is precisely the sort of thing we wished to prevent. I do not mean to be too harsh. I commented upon that answer, and I do agree in part with the response provided with Sven Yargs and user in that there is some value in comiling resources to demonstrate the current state of affairs to demonstrate a present lack of consensus. However, at the same time I believe this is moreso the responsibility of the question than an answer to one, and especially so if the answer does not even attempt to express the conclusion it is trying to support, and why the competing theories are all equally plausible.
Do remember that the help center guidelines for referencing material written by others in an answer requests that we do not merely copy text from external resources, but use select portions to support our own hypothesis. Our contributions need a somewhat personalized touch in order to truly be ours.
Most of the people we are trying to help are not the direct questioner, but people who share the questioner's concern doing a search engine query that will lead them to the webpage. I think that we should leave the impression that we are a distinctly useful resource that is worth checking to them.
Now I agree that sometimes even the best of resouces are not enough. I may even agree that questions of origination are a matter of continous research that can not be "definitively and permanently answered". However, we have to have a reasonable expectation regarding what constitutes "enough". When a presumptively correct and readily available answer exists, disaster can still strike.
People will exercise faith in the best of resources which are assumed to have rigorously researched the matter, unless it is shown beforehand that any pre-existing available information is inadequate, so these sorts of questions may garner many votes for them under the presumption that they are correct.
When this is at its very worst, what we end up with is a potentially wrong answer that has an overhwelming amount of consensus expressed through faithful votes, and accepted by the user, making it practically pointless for anybody to try and write a better answer to compete with it on our website, because it will be little viewed and perhaps forever doomed to live in the shadow of the overrated answer.
When it is at its very best, the answer is correct but this is optimizing for sand, not pearls and detracts from the distinct usefulness of English Language & Usage as a resource. It also fills the internet with needlessly redundant information, making the truth just that much harder to research because our search result may push a better one down a rank, and displace it onto another page. These are still undesirable consequences.
When a direct answer to the question does not already exist, this is not as much of a problem: There is no general reference to exercise faith in, so people trying to answer the question need to thoroughly explain their own hypothesis and exercise some effort in compiling their own evidence to prove why it is likely to be the best one.
When questioners include the research themselves to it establishes a minimal standard of evidience. It means an equivalent resources is dissatisfactory to submit as an answer all on its own, because it may be no more truthful than what they already provided. The accepted answer will probably require more thorough treatment, and the people auditing the answers may have an idea that the post is not exactly doing anything to actually help address the concern.
In either of those cases, I would personally grant a question impunity from this type of closure because for all practical intents and purposes, the problem is solved. However, I can not say the same about unilaterally imposed edits.
Correct me if I am wrong, but "softball" research by editors does not seem to actually fix the problem much at all. It neither disproves the existance of a problematic general reference answer, nor does it inform us as to what the questioner considers acceptable evidence. Because of these considerations, I would only propose that we edit questions to include research if we can thoroughly prove that the question is presently unsettled. I do appreciate that you were not trying to make an overly transformative post, but by editing in intentionally weak research, there is a considerable risk that a general reference answer will become the accepted answer because the questioner who did not do that research is still in control. That is purportedly the very last thing that we want.
Other Thoughts Regarding Proceedure
If our proceedure does not effectively address the concerns we meant for it to address, then we may as well not have the closure reason, for lack of any practical purpose. It can only serve to obstruct potentially interesting answers from being given to potentially good subject matter. We should not be doing something so harmful unless there is an overriding benefit to us, such as the ones aforementioned.
That is not to say I do not sympathize with your concern that we may be overly zealous with our closure reason. Similarly to your concern for questions of origination as a matter of continous research, I wish people took word comparison questions more seriously, since those often do not have any sort of directly documented answer. The dictionary is not at all designed to directly compare words and it almost always takes some extra work to explain out what difference the definitions impart, if they even address the concern at all.
However, despite that and the fact that I think the most commonly checked resources may be in error, I would not encourage reopening a word-comparison question if my cursory research had shown that the question was already addressed by a commonly available existing resource, such as a dictionary of usage, unless I had a reason to suspect that the given answer was wrong and wanted to add my own answer. I do not see you answering the On the Nose Question, and I do not know the full extent of why you so for all we know the Phrasefinder's answer may be the best information currently possible, particularly since it makes reference to a specific dated document, and may be treated as such unless otherwise is proven.
As such, in the future, what I would advise that if you want to have a question reopened without cajoling the questioner into editing the question themselves, that you do is perform a reasonably thorough research effort demonstrating your interest in the question, and consult meta with your planned edit to determine if your interpretation of the post is reasonable by consensus. This way, critical eyes can audit the proposal and determine if iyour proposed edit honors the meaning of the original question, and meta has the chance to audit whether or not the edit solves the problem.
This is what I tried to do when I asked if Why Can We Use Inadequate but not Inspecific should be reopened, and I only took action once I got the go-ahead after waiting for a consensus to be established.
My reasoning is that if I include a better source I also have to explain why it's not good enoughI disagree, if you find two or more conflicting sources with different dates that makes the question so much more interesting and a challenge. Another reason why I didn't jump to reopen is b/c it looked boring. And before anyone says a word, I didn't cast any vote to close it.