My inverter's instructions make a big point to NEVER run the chassis ground lug wire over to the inverter's own neg input terminal (which goes back to the neg grounded battery) but run it straight to the frame.
Even though there is a path through the frame back through the battery (also frame grounded) the direct inverter frame ground seems to be ok under the rules.
I got lost in the OP :) but there may be a variation on this no-no there.
The purpose of the inverter's chassis to frame wire grounding is to reduce radio and TV interference. The inverter will run just fine without the chassis ground being connected.
An intermittent GFCI issue may be due to a loose connection somewhere?
