I was hoping that it would trigger an insight in someone who might solve this mystery for me. As I said, I'm not sure how to develop it into a full answer myself (but it might be related to this other vague/possibly-absurd idea).

Perhaps I'm abusing this community by presenting ideas that are half-formed and "epistemically unhygienic", but I expect that's not a serious danger. It seems like a promising direction to explore, that I don't see anyone else exploring (kind of like UDT until recently). I have too many questions I'd like to see answered, and not enough time and ability to answer them all myself.