I finally got some new solder in and reflowed a bunch of the joints you pointed out, and flipped the diodes around and… it all works!
The IPA is liquid magic. That and a toothbrush cleaned the shit out of the board, almost to the point that there was a thin layer of flux residue on everything. I had to keep cleaning the whole thing off, then more scrubbing, then more wiping down, to get the coat of shmear off the whole thing.
Thanks so much for your helps in this thread! (@okyeron, @Nordseele)