I replaced all the caps except two -- I was so concerned about making sure the replacement big boy caps were short enough to fit that the 470µF I got is about 50% too big for the footprint. And I left the original 0.1µF because DigiKey doesn't have them (or else I couldn't find them). 

Anyway, after screwing the board back down and reconnecting the fiddly-ass ribbon cables, she powered on but didn't type. So I retried the keyboard ribbon cable about five times, and it finally worked. Hooray!