The headline reason for this post is to ask for Each other’s work or each other’s works? to be reopened, but if possible I'd also like to know why it was closed.
I find it hard to believe "lack of research" could meaningfully be cited as a closevote reason. I personally was quite surprised to discover from NGrams that even with the more straightforward context They touched each other's nose/s, the plural is preferred (where I would probably have gone for singular nose).
But the actual context cited by OP was far more complicated, given that He's a great artist! I really like his work/s carries almost exactly the same sense regardless of the plurality, whereas it would be nonsensical to say She's got a great face for a model! I really like her noses!
Also note that I don't think my comments under the question really explain much. Since I personally would use singular in both cases anyway, I'm probably not the best person to explain why most people don't do the same as me!