Time to rebuild?
I took the choke thermostat off the manifold, sprayed the coil with WD-40, and reinstalled it. The good news: on the next cold-start, the idle was so much higher that I backed the fast-idle screw way out. The bad news: apparently I backed out the screw too far, because now it's completely gone. Ugh.
So I'll probably get the electric choke conversion to replace my rusty choke coil (and a new fast-idle screw), but I'm sure the choke wasn't the only problem.