Update-

It's looking more and more likely to be a clutch issue. I changed the
transmission fluid; it did get a bit smoother, but it isn't nearly as
smooth as it used to be. If I push the clutch down really hard, it
improves a bit as well. I don't have much experience with manual
transmissions, so I don't know how fast they break down. I'm at just
over a hundred thousand miles, so she's probably about due....
What kind of problems can occur in a clutch? It seems to me (and my
little experience) that there's no problem with the clutch hydraulics,
because pressing it in is as smooth as ever. There's no odd noises
from it either, so I just don't know what it would be.
Thanks for all the help.