If I'm reading your info correctly the problem is on the line going to the outlet in the engine compartment where you plug the block heater into. If the outlet is a GFI I'd replace it... probably with one that is not. Yes I know a GFI was put there for a reason... a dumb reason.
Even if it's below 0 you do not need the block heater. Turn the key on and when the wait to start light goes out, turn the key off and back on. This will let the grid heater heat some more and when the light goes out you should be able to start with no problem.
If you still feel the need to run the block heater, run a separate extension cord from your house or the pedestal directly to the plug for the heater several hours before wanting to start it.
About the only thing I use my block heater outlet for is to run power to another camper or to power a 120V item at the back of the MH as I have a short extension cord on the outlet so it's easy to plug into. Yes I know I stand a chance of being shocked, but for 40 years I survived without GFIs and most of the tools were not even insulated and the plugs only had two lugs... not grounded. Granted I still ground my arm before turning things on.