Okay, this morning's investigation:
Continuity along paths to the floppy look good. I've tested paths from all pins on the 1772, be it the 1772 to a wire stuck in the other end of the ribbon cable, the 1772 to the 7406, the 7406 to the other end of a wire stuck into the other end of the ribbon cable, the 1772 to the DMA, or 1772 to 5v/ground/reset. All pins in and out of the 1772 look like they have continuity to where they should. All lines on the ribbon cable that
should be connected to something appear to be connected to that thing. (I haven't exhaustively checked lines to/from the DMA yet. The main data lines appear good.)
Also I opted to try the DMA pull-up fix mentioned up-thread. On the bottom of the board, I've thrown in a 1k resistor network. I've done the same as far as I can tell from what I see in other photos.
PXL_20220417_151935834.jpg
(It's not clear in the photo but the top pin broken out is indeed the one marked as pin 1, and the resistances look good so I know I've got contact on the 8 other pins.)
And the result is: no change!
I've never had an "untested" purchase so stubborn as this one. :D
So far I've neglected the reset fix, and at some point I'll have to try it. (So far I've declared it unrelated, but, fewer other options remain.) I haven't tried the 1772 pull-up fix yet either.
Editing to add: this purchase was deliberately bought untested, so if it never works, it's not a loss. I bought it figuring I'd use it for parts. Floppy aside, it was clean enough and booted so easily that I've been compelled to see if I can make it fly again!