I got up early and soldered the DFN HC595s and 0804 resistor packs before heading to work:

I used braid to clear a few obvious bridges and checked resistance pad-to-pad across the resistor networks. They were a bit fussy to solder because of the aforementioned circuit carving gore; I had to reflow a few of the pads and one of them ended up needing a tiny length of bodge wire to bridge a gap in the copper. But after not too much work each trace beeps out as it should and I didn't detect any bridges between adjacent nets! The other stuff (LEDs, a few bypass caps, the ESP32, and the SAO header on the back) is pretty low-risk, so I don't anticipate any issues with getting this woken up this evening with a few hours to spare. Huzzah, etc