So, now I have a report.
I worked on the original circuit board for a while and got nowhere. I think that I really screwed up 3 connections. I have not thrown it into the garbage, and will buy some of the trace re-builder to try to fix it. I attempted to scrape away some solder mask and attach a very thin wire to that and the leg of the switch. It appeared to work when I soldered it, but the connection never "took" for some reason. Since they all work except 3, it will be shelved to my "project" list.
I dismantled another AT101W that was laying around (luckily, I had 3 that I would have sold, but you can hardly get over $15 + shipping on ebay, maybe $20 if you get lucky, and for that I would just as soon keep them) and started removing black Alps switches. Whoever built that board was much more zealous about bending the legs down, if the first one had been like that I would have wrecked a dozen switches instead of 3.
So, there were 4 pads that looked questionable, but they were only partially peeled up, not off altogether, so I was very cautious around them. I installed all my new switches, and only 2 did not work (both orange, luckily). I pulled them and tested them, one was OK and one was dead. So I replaced one and carefully put them back, and everything worked great!
Attached are photos of the project. The reason for the mix of orange and blue is that I had 88 blue switches (87 really, one was no good) and I wanted to be able to stretch them to populate 2 keyboards, at least for now.
I had 2 keyboards' full of orange switches, less a small handful that were no good, so I had all the "fillers" that I needed.
The best technique on the aggressively bent legs was to use a small flat screwdriver in one hand and the soldering iron in the other, and bend while the solder was soft. I used the solder sucker before and after this process, so the whole thing took a lot longer than the 2-step suck-and-pull I tried last time.