Solution 1:

What a great observation. I’m not aware of any linguistic literature on this (but I’ll post an edit if I come across some).

A few comments on the data:

First, I’d be careful of using coordinated pronouns (you and me) to illustrate the core problem, as people have wild ideas about what is normatively sanctioned and this often affects their judgments. I think a reasonably safe frame would be Anyone who likes X’s answer would be “yes”; e.g.:

Anyone who likes butter’s answer would be “yes”.
Anyone who likes running’s answer would be “yes”.
Anyone who likes cats’ answer would be “yes”.
??Anyone who likes me’s answer would be “yes”.
??Anyone who likes you’s answer would be “yes”.
??Anyone who likes him’s answer would be “yes”.

Second, the effect applies to demonstrative too, I think:

??Anyone who likes that’s answer would be “yes”.
??Anyone who likes these’(s) answer would be “yes”.

Third, I find these all slightly to quite uncomfortable, rather than crashingly bad.

This last fact might be significant, as it suggests a parsing, rather than a generation, difficulty. Pursuing that hunch, I’d look for an explanation in ’s’s being a determiner. Part of the motivation for treating ’s as a determiner is the complementary distribution between DP’s (e.g., John’s, the policeman’s) and the, personal pronouns, and demonstratives (e.g., *the policeman’s that hat). Significantly, these last two sets (personal pronouns and demonstratives) are what ’s attaches to in the preceding ‘??’ examples. As nohat observes in the comment on your question, ’s attaches to the whole phrase. But that’s at the semantic level. In linear terms, it encliticizes to the last word the phrase. It appears that this encliticization process doesn’t like moving a determiner onto another determiner (which is reminiscent of Norvin Richard’s findings on linearization more generally). This may be getting a bit technical, so I’d better stop; but I hope that gives you some ideas.

P.S.: I find a difference between weak and strong pronouns. Anyone who like hím’s answer is worse than Anyone who líkes ’im’s answer.

P.P.S.: Of course, copular ’s is fine in all of these. Anyone who like me’s going to answer “yes”, Anyone who likes you’s going to answer “yes”, etc.

Solution 2:

I think you've already said most of what's to be said about this, aside from the obvious fact that these pronouns have their own possessive forms.

I think this is related to a phenomenon called blocking, whereby we avoid creating regular forms when there is an irregular form available. In your examples, of course, the irregular form isn't actually available — we can't say *"you and my picture" — but such situations are not unheard of.

For example, consider the verb stride. It has an irregular past tense, strode . . . and basically no past participle. I assume that if it weren't for the irregular past tense, then the past participle would just be *strided; but strode seems to have somehow blocked that option, leaving an odd gap. (Quite a few dictionaries claim that the past participle is stridden — compare drive/drove/driven, write/wrote/written, ride/rode/ridden, rise/rose/risen — but in fact stridden is vanishingly rare, as are all likely alternatives.) (This has been remarked upon many times independently; see "When you stride away, what is it that you've done?" on Language Log.)

It can be hard to predict what will and won't be blocked, and it may vary from speaker to speaker. You give ?"the gift I gave to them's receipt" as one of your ungrammatical examples, but I don't find that to be much less acceptable than ?"the gift's receipt". I find something like "One of them liked us, but the rest hated us, and the one who liked us's wife was one of the worst" (made-up example) to be pretty acceptable, at least in speech.

For a better-studied case where different speakers differ in terms of blocking, consider the baseball jargon phrase fly out. In baseball, a "fly-out" is when the batter successfully hits the ball, and hits it high, but someone from the other team manages to catch the ball on its way down, knocking the batter out of the inning. [link] This phrase is often verbed — so, "to fly out" means to hit a fly ball but then become out because someone caught it — raising the question of what past tense and past participle to use. Some linguists have argued that native speakers will naturally use the regular form, flied out, because this clearly isn't the ordinary verb fly. (This case is made in a 1992 paper, "Why no mere mortal has ever flown out to center field".) However, the data are actually ambiguous; many native speakers do prefer flew out and flown out. (This point is made in a 1993 response, "Why no mere mortal has ever flown out to center field but people often say they do".) In fact, it seems that nowadays the "flew out" version has almost completely won out: "flew out to left field" gets thousands of Google hits, whereas "flied out to left field" gets only nine.