A buddy snaked an extension cord (female end) out to his camper bumper and stored it "in the bumper" so he could pull it out with the plastic end cap.
Then he cut the male end off the cord and wired it to the inverted. When he goes boondocking he has a $25 120 volt 20 amp to 50 amp converter (The thing you twist onto your RV's 50 amp plug that lets you plug it into a regular extension cord. And just plugs that female end into the existing power system.
All he had to do was fish tape an extension cord inside the camper to the back end and out a hole he then sealed with epoxy or whatever. drilled a hole in the bumper and get it in there (with plastic grommet so sharp metal don't screw it up) and then left enough wire in the bumper to plug into the normal power inlet.
This is exactly the way your are getting a ground fault (which by the way is often a bad hot water heating element. you will actually have to unwire the element (turning the breaker off won't work) to test if that is the source of the ground fault, just fyi. Also did you make sure your "hot side" E.g. line and neutral are correct that might set off your GFI as well. e.g. you have the two wires wired backward into the inverter (on the output side) one should be line and one neutral.