As I read this, one thing comes to mind and I am not surprised that ScottyDoggs named it. If you are losing power, it has to be a ground issue.
All my GP's are 6th Generation, but many of the components are the same with the '04+ GP's. When I have had any kind of power issues, I always carefully looked at the grounds and would always find a problem somewhere. The most recent case was with the negative battery post which was stripped out on mine. I see you checked the battery post already. On another GP I no longer own, it was the ground wires on the front of the transaxle (as ScottyDoggs mentioned). There was a good bit of filth from oil and coolant all around the area where the ground wires are bolted on, and upon removing them and cleaning them, I could see how there was not true contact to bare metal. After I fixed that up, I had full power back and never had problems again. (previous owner messed that car up pretty bad)
The voltages at the power distribution box will not tell you too much.
Do you know if the car was ever in a flood?
I would find and trace all the ground wires and make sure that they are intact, and are making proper contact.
