Hello all.
Apologies for the lack of response... I got it fixed, but still have no idea what happened..
I thought I had narrowed the issue down to the relay in the pic below (always connected), but in my fiddling I accidentally shorted a connection and popped the 30A fuse. I also had a problem with the mechanical timer (which I pulled out and fiddled with), and once it was all back together, the issue no longer happened.
So I don't know if the issue was the relay, or if the micro-switch in the timer was stuck on...
On the up-side, I have learned a lot more about my tub, and it seems to be running fine.