Grouse, did you get this figured out? I have a 05 Rainier with the exact same problem, albeit instead of at 20 degrees, it happens when it gets below 0. I’ve done some test of my own to try and diagnose.
Rear was completely down, fully sagged.
Cycled ignition to see if could raise it; pump runs for 20 secs then turns off. no movement of rear height at all.
Tested air pressure at the toy/tire inflation valve inside the truck. it would reach 10psi then stop there. this told me it has to be a relief valve stuck open/partial since the pump ran fine normally.
Due to fact that I had no issues above 0 (this latest cold snap is what caused the issue) I assume warming the pump would help.
so put heater under the pump and got ambient air in garage to 33 deg.
cycled ignition and pump ran extended duration, and rear end went to normal height.
went to bed at that point.
came back in morning, and height had not changed. so this tells me the valve is closed and bags/lines are not leaking.

This sounds very similar to what you spoke of.
Only thing I can find is a kit that seems to be able to replace the relief valve seal and spring on side of pump. curious on your thoughts on that.