Hi ,
Welcome to the forum.
This can be a difficult problem to trouble shoot. A bad or failing bisquette burner will cause the GFCI to trip. Try running the smoker with the bisquette burner off for a while. If it runs fine without tripping the circuit, then next turn on the bisquette burner. If the circuit trips, then a bad bisquette burner may be the problem.
When you cleaned the generator, did you check to make sure there was no worn insulation on any of the wires, corrosion, or loose connections?
If you have too many appliances running on the same circuit drawing too much current, this can cause it to trip.
Too long of an extension cord could cause the problem.
GFCI can degrade over time, and can fail. If your GFCI is more than 10 years old it may need to be replaced. I had to replace one that was about 12 years old.
There is more information about GFCI's tripping - on this forum, but the search function is not working at this time. When search feature is working again do a search on GFCI.