Well... Three years later I have some new information. I have taken no action and just lived with the situation the way it is/was.
New findings: Contrary to the post title. Whether on AC or LP everything freezes. This is regardless of thermostat knob position (even in the "off" position). Unless it's REALLY REALLY hot outside day and night. Then it pretty much keeps up fine. Cooler days and nights? It freezes.
I gave up using it on 12V. Not worth my time and aggravation. It may or may not work.
Hopefully still waiting on some updated schematic documentation.
