I've been testing out some things with the pump, in waste mode, in order to drain the pool for closing time.
I'm able to run it on high speed for about 30 seconds at first, which gets the pump pretty close to prime (the basket never completely fills with water.) The thermal protection mode will click on (audibly), but it somehow still runs, albeit slowly. I'll then flip it to low speed mode, where it seems to operate normally, both audibly and operationally, until the high speed thermal protection clicks back to normal. At that point, it'll run on low speed but in a way that sounds pretty horrible. It won't run like this for very long, popping the low speed thermal protection mode on after a few seconds.
I managed to figure out that once high speed (effectively) shuts down, if I flip it to low speed and let it run until the high speed thermal mode goes back to normal, if I keep flipping the speeds back and forth as soon as the high speed thermal mode returns to normal, I'll be able to keep the pump running continually for a good while. I was able to drain a few thousand gallons of water today, which is getting me closer to being able to close the pool for winter, and then deal with this mess in the spring.
I don't know enough about motors to know what is going on with it right now, but maybe this might mean something to someone on here.