An update:  I swapped a couple keyswitches, and it's definitely the switches and not the board or ROMs.  A hot bath didn't do anything.  However, I've been able to get most of the keys back by pressing hard and wiggling it.  I'm guessing there's some corrosion in the key switches.  Maybe from humidity?  By pressing and wigging, I'm guessing it's scrapping at the corrosion and making contact.  I'm going to continue doing it, see if I can get all the keys working again.

The manufacturer sure used high quality solder.  Even after all these years, the solder on the switches melted like they were just soldered on.  First time I've ever encountered that.

Just used a pair of tweezers and the switch comes right out.  I found it rather easy.