Okay, moment of truth. Is the replacement theory true?
And regarding Karin's wish... What if it was for Yuu to move on from her and find someone new? That works decently well in the confines of this theory, I guess. Because even though all these Karins are "Machihashi Karin" they're also all obviously different people. With this many, there's no way anyone can claim that these are legitimately all just parts of a single whole.
Like, even if replacement theory isn't true, (this is almost certainly the case) to say that the original split apart just does not make sense anymore. There is just no way that that's what actually happened. A single person just is not this multifaceted. (A manga character especially!)