Thinking about this more, I guess my analysis is basically equivalent to a metalinguistic construction, maybe not limited to nouns at all:

Imagine describing a scene as director for a movie:
"Yellow is fine."
"Happy is fine."
"In the corner is fine."
"Both is fine."
"Quickly is fine."

Maybe even literally metalinguistic as in a writer correcting a draft:
"And is fine."
"Went is fine."
"Goes is fine."
etc.

I'm not sure to what extent the noun phrases in the original example (and the others discussed above) are more like normal subjects than the obviously atypical examples given here, but I think this may be the same reason why plural agreement doesn't apply.

I wouldn't say they involve ellipsis (which I see as a specific syntactic operation in a generative sense), but they do involve/require context. If we coined the term "discourse ellipsis" then that might fit. Similar to how fragment answers work, but in this case there is no full linguistic structure to refer back to, so I don't know that they'd still be literally "ellipsis" rather than just fragments -- that is, concepts rather than declarations.

Indeed, quotations might be needed as punctuation-- I was thinking of just pronouncing those words, not how to write it out (I'm not sure such sentences would really appear in print).

So is it the case that those examples require quotes, but the plural subject NPs discussed above in this discussion do not?

As I said, I don't think that "Two doctors is fine" is literally metalinguistic, but it's something along those lines-- mentioning, rather than referring. Playing with the compositionality of language.

For similar reasons I'm not certain that quotes are needed on all of the examples in my previous post, although I would be more likely to agree for those than for the plural-with-singular-agreement noun subjects.