OK, I did a bench test on the starter by securely placing into a vise and applying voltage to the appropriate leads. The shaft extends quickly and without any binding or resistance, but it doesn't turn a bit, which is exactly how it's behaving in the car.
So, I started taking it apart to see if I could see something obviously wrong with it. When I removed the rear plate, exposing the commutator and the magnetic brush assembly, at least one of the brushes was laying inside the body of the starter, outside of its mount piece. This could clearly be the cause of the starter not turning, but I don't know if the brush fell out on its own, or while I was pulling out the plate that the brush assemblies are attached to.
So, has anybody here ever rebuilt a starter? I ask because this brush assembly is one miserable contraption. The brush mounts kind of rest in slots in the assembly without really being firmly attached, and of course there are springs that push the brushes toward the commutator which make it very difficult to keep the brushes in their mounts. So the whole thing is composed of over a dozen pieces which all sort of flop in the breeze, with springs trying to keep everything apart, and the whole thing is somehow supposed to fit inside the starter body, which is a very tight squeeze. I thought the seat switches were unnecessarily complicated, but this makes those look like a clothes pin. I can't for the life of me see how to put it back together. If anybody out there has ever done this, please let me know how you did it. My new starter is supposed to ship on Friday, so if I can't figure out how to put my old one back together, I'm going to forget about it and just put the new one in. Thanks.