I'm not clear what you intended when you wrote "plugging the inverter into shore power with an extension cord right to the dock outlet". That would fry the inverter. I assume you meant to plug it into the external shore power outlet on the boat?

That would still involve more than one GFCI. If I plugged it into the shore power inlet I would only change which side of the shore power breaker panel the second GFCI is on, but there would still be 2 GFCI's in series, and that was my original question: Whether 2 GFCI's should cause one to trip?