I would start with turning off all breakers at the 120 power panel. Run the generator, then turn on breakers one at a time.
If the converter blows the GFCI, unplug the converter. Remember that the GFCI in the kitchen may also protect all outlets further past the actual plug point.
Use some extension cords from shore power with a GFCI protected circuit to see what happens when you plug the converter in there.
Isolate the problem first. Maybe the leads on your power panel might have a loose connection. All hots, neutrals, and grounds have to be tight.