Gas Oven Keeps Tripping GFCI (Moisture?)
It's your fan/motor... 

Motors are common causes of GFCI trips because of insulation breakdown.  

In your case it could be simply that.  However, given that the fan's job is moving air which is particulate-laden, it is rather likely that the particulates in question (or merely dust in your house made sticky by food grease) have accumulated on the motor.  The cool motor draws up hot, humid air... and condensation occurs.  This wets the particulates.  This makes them a good enough conductor to induce a ground fault and trip the GFCI. 

You could clean the fan motor area and hope for the best.  The problem may be deep inside the motor in an area impracticable to clean.