Kyle,
I'm not an electrician (mech engr) but I don't think you're tripping the GFI because of overloading the circuit. That would trip the circuit breaker. Symptom would be that the smoker runs fine until you turn something else on that is on the same circuit. Check the label on your smoker to see how many watts it uses....mine is 250w at 120V so only about 2 amps. The GFI is detecting a current in the ground circuit. The GFI outlet itself could be bad (or installed incorrectly) or you've got a problem with both your smokers. Does plugging anything else into that outlet trip it? If everything does then its probably the outlet, if not check your power cords per my previous post.