How many pumps on the grease gun does it take to fill the inside cavity and not push out the axel seal? I think this is an unsafe system and should never be used. I think over weight is safer than no brakes and I'm not into overloading either.
The brake cans with the big spring is in the rear. You have a rod with a pin through it check that the pin turns free. If not this is the cause of your problem. The rods should be the same lenght from left side to right side. The side with the locked brake may be longer than the other. If so back off on the slack adjuster.
I think I would put thermostat back in living room and use a small electric heater to help heat the bedroom. We use electric heater to heat the whole camper. The only time we use furnace is when boondocking or no electric . You could try adjustable floor grills to help even the furnace heat.