I know this thread has been idle for a few months, but these GFCI nuisance trips are an ongoing issue for a lot of folks.
In a few cases where I have helped others troubleshoot this issue, the problem has always been isolated to current leakage between the heating element and the outer grounded coating over the element.
Since heating elements are sealed up it is not obvious by just looking at them, but the outside metallic sheath is insulated from the internal resistance element that gets power.
The high temperature insulation can degrade over time or absorb moisture. When it does, the insulation will develop a leakage current path to the outer sheath. When it does, it can trip a GFCI.
It doesn't take much current leakage to trip a class A GFCI. 5 milliamps is all they are rated for.
I usually just check the heating element first. Disconnect the power wires going to the element, connect an ohmmeter between either one of the element terminals and the other to the cabinet ground. The meter should read infinite resistance or OL. If it reads any resistance at all, there is an internal leakage path inside the element to the outer sheath.
Sometimes the leakage path that causes the GFCI to trip is caused by absorbed moisture inside the heating element. Moving the smoker to an outlet without a GFCI and powering it up for a few minutes can heat up the element and drive out the moisture.
Once the moisture is driven out of the element, the leakage current will be low enough to allow operating the smoker on a GFCI protected outlet. If the leakage is from some other cause besides moisture, this hack won't work.