since the GFCI is very sensitive for what it does, and a 'ground' could easily cause it to trip, I imagine that either there is a grounding issue with the circuit, or, because it is a circuit tied into/out of the Inverter, that something about how the inverter is installed/grounded is suspect.... while many of us don't have these issues, I imagine that it can be VERY FRUSTRATING for owners who do - my hats off to you for putting up with it, and getting 'creative' in how you handle it!
'14 Palazzo 33.3 bunkhouse 34' diesel
KingTailgater2 Dish HD, 100w/5a SOLAR, BlueOx
100,000+mi since '14 - US, Alaska, Canada - Northwest, GA! (also, '14 Gulfstream Amerilite and '07 ForestRiver Rockwood) : )