We did call a plumber, in fact. The seat was removable but it was
completely stripped and he had a hard time getting it out. He used some
tool that was a tapered threaded stick - perhaps it was reverse
threaded; I don't know ("if you want to watch, it'll cost extra; if you
want to help, it'll cost even more"). He showed me that it was badly
corroded and had a notch out of it that would never make the seal.

There was no way I could have removed it myself; definitely worth it to
have someone with the tools and the expertise come and do it. In fact,
he replaced all three stems and seats, for $187. They were all pretty
messed up; it was amazing that the hot hadn't begun to leak yet.

It was a great learning experience for us (thanks to help from
resources like this group and the kind and encouraging people here and
elsewhwere); glad to have things back up to speed beyond what we could
do. Part of it is the tools, mostly it's the experience.

I guess our water has a lot of calcium in it and the deposits can
really play havoc with the fixtures.

Another thing I learned - the sleeves that come out of the wall are
removable (who knew?!) but it took a lot of wrenching with a big-ass
wrench for the plumber to actually get 'em out. I would have assumed
they were part of the permanent install and wouldn't even have tried,
but it's certainly easier working with the stems etc when you can get
right in there!