I would definitely try to determine why the GFCI is tripping. The first thing I would assume is that it IS tripping because of a ground fault somewhere. Did you have the 30 amp main breaker in the panel off too? If so and it tripped, I would disconnect the neutral inside the panel and see if the GFCI still trips. If it does, it's somewhere between the end of the shore power cord inside the panel and where it plugs into the GFCI recept. Is it a detachable cord? If so, you might try to borrow one and see what happens.
Did you have the 30/20A adapter plugged into an extension cord or directly into the GFCI recept.? Does the GFCI trip if you remove the shore power cord from the circuit? What does the shore power plug and adapter look like? If dirty, clean as needed including the prongs. Maybe just toss the adapter out and get a new pigtail type.
There is always the chance that a GFCI recept. is tired or defective. You might try using a GFCI tester (under $10 at HD).
Do all the 120 volt circuits work okay on the 30 amp supply?
If it's an older TT and has been sitting unused and maybe in the elements, I would check the connections at the battery and to the frame. I'd also check the 12 and 120 volt connections at the panel including the 12 volt grounds behind the panel. Check the tightness of all the breaker terminals and 12 volt connections in the panel. Good to do on an older unit regardless.