So, here's what I think happened - the speedo was from a junkyard ES, and I think it hadn't moved in a long time. It spun fine when I tested it, but the part that connects to the speedo cable seized after driving for 10 miles or so. I think that it was dry from sitting too long. When I took the speedo out, it was stuck. I used some light machine oil and after a while I got it to spin again, but I don't know if I'd put it back in the car without a lot of testing.

Anyways, when the speedo seized, the cable held strong, so the nylon gear inside the transmission lost its teeth. Incidentally, the transmission speedo gear looks like it's the same between 1972 and 1973 automatic ES cars. I replaced the shredded gear and put in an old spare speedo and everything is working again. Thanks for the tips!