I tried resoldering the pots in the PBU over Labor Day weekend. They appeared to be a bit loose, but alas, no change in behavior.
One night last week I finally got around to rummaging under the hood and disconnecting the aux water pump. It conveniently has an electric plug which can just be undone.
Result - perfect! The temperature is correctly regulated, no blasts of hot air. Ran the a/c on a 60F morning. Compressor was cycling on and off, discharge air was about 55F, car was comfortable.
Now, I may have to replace the pump later, we'll see how the heat works this winter. But for now it's all copacetic. Total cost: $0.00. My kind of repair.