@qno, I’d be interested to hear if you have a take on the Eternal Question. (Which is, of course, the question of why other characters besides Rika and Hanyuu can vaguely remember other worlds if the worlds are completely separate.)
In the Keiichi Maebara thread, I hinted at a new theory I have when I said
Depending on how the worlds work, [Rika] might even be “dragging” [Keiichi] from world to world.
If we assume that Rika is, indeed, dragging Keiichi from world to world, then we could kill two birds with one stone: we could reconcile almost all of the contradictory evidence concerning whether the characters are the same people from world to world, and simultaneously explain why Keiichi has more memories than anyone besides Rika and Hanyuu.
Because I realized that almost all the evidence supporting the characters being the same people is referring to Keiichi in particular. (If asked for, I can provide examples.)
As for the other characters’ memories, you could look at it as Hanyuu transporting Rika, Rika dragging Keiichi, and then Rika and Keiichi eventually dragging everyone else. (I’m including Mion and Satoko even though they don’t have any memories of other worlds (that we know of), because the ending of Minagoroshi strongly implies that it’s at least the same group of people in Matsuribayashi as in Minagoroshi.)
As for Akasaka, him remembering other worlds seemed to be due to something Frederica did in the sea of fragments, so I consider him an exception.
As for why and how Rika would be dragging Keiichi, I already went into that in the Keiichi Maebara thread, so here I’ll just say that Keiichi is basically Rika’s piece.