Riddle me this, inverter

I agree the first isolation step should be to plug the RV into a different GFCI outlet, using a different extension cord and adapter if possible, and see if it trips. Is this the older Freedom 2000 that has an MSW output? If that were the case, you could have leakage somewhere that is is greater with MSW than with PSW. If I were isolating this I think I might go through the standard GFCI trip isolation steps of also disconnecting the individual circuit neutral wires. But it's easiest to start with pluggable things like the extension cord, adapter, and power converter and refrig, which in some cases are plugged into outlets in the RV.