Does that "1" seem to be the overload indication? It may be. Just a "1", but with no other characters showing?
That might be the overload indication, but you'll have to read the manual for the meter to find out. Different meters display overload differently.
To me, the easiest real test here is to see if another new GFCI trips when you plug the smoker into its protected outlet. Back in the day I could get these at Pay-N-Pak for about $5. They're a little more now, but here's one at
Amazon:
Use your extension cord setup to reach a non-GFCI outlet, but put the new GFCI adapter between the extension cord and the smoker, or between the extension cord and the outlet you've plugged it into (NOT the GFCI outlet you've already been having problems with). Then fire up the smoker. If it trips the new GFCI, you know the smoker has a problem.
This will be much more sure-fire than trying to test for the leakage path yourself. To truly test everything you'd need to test will be quite difficult. The new GFCI adapter will do the test for you with the smoker actually powered up.
If the smoker does have a ground fault, you will need to have it repaired IMO. I wouldn't want to continue running it, even if I could by using a non-protected outlet (via your extension cord). It might not cause a problem right away, but basically, the GFCI tripping is telling you something. Something you don't want to hear, but something nonetheless.
On the other hand, if the smoker does NOT trip the new GFCI, then you'll know that your old, existing GFCI may be the problem. So that's good to know, too.
Sorry I haven't checked the forum for a while. I hope this helps.
