Won't Drain Code F02 Motor Clicking then Overheats

My older (2003) Kenmore Elite HE3 washing machine has started giving me a F02 error and not draining.

I have cleaned the basket, wasn't dirty. We checked all hoses and they are fine.

We noticed that it does a single load fine. If I run a second load immediately (or have loads with pre-wash/extra rinses) it will not drain correctly on the second load. I know that it will fail when, instead of hearing the drain motor whirring, I hear a plastic click, click, click over and over again. Kind-of like a piece of plastic in a slow-moving bicycle tire. It seems to try to run over and over again and then just stops and gives an F02 error code. If I let it sit like an hour, it will run fine again.

I think that something in the motor is coming lose when it is too warm (but not overheated) and it is causing the motor to keep running until it overheats.

Does anyone have any experience with this? I'd like to confirm my suspicion before I go out and replace the motor as it's expensive ($100-200). I don't like the idea of throwing away something that might just need a repair, but I don't want to spend the money if it won't fix my problem or if it will start to turn into a money pit soon (we already replaced the inlet valves on this machine about 3 years ago.)