You liked this question, but didn't answer it:
Does it trip when plugged in, or only when turned on? If the former, I'd open the junction box and take a look.
Unfortunately I did not think to test that while I was there, I will when i go back.
I think doing what Larry said is important because if it trips when it's plugged in without it being turned on, then the tripping is being caused by a constant leakage current (and most likely from capacitors tied to the EGC for EMI reduction, as others have said).
But if it only trips when the appliance is turned on, then the tripping is likely caused by a VFD or other switching electronic devices within the unit as Hal mentioned.
Of course, capacitors could be contributing some leakage current even if it's not enough to cause the GFCI to trip by itself.
If the GFCI trips without the unit being turned on, then I think the following test could help confirm the root cause of the leakage, as long as there's time available to do such a test:
Assume that a capacitance of x μF inside the appliance is causing a leakage current I
L to flow from the GFCI's load side hot terminal to the EGC. Then if a capacitor with the value x μF is connected between the GFCI line input hot terminal and the load side neutral terminal, then a current I
L will flow back into the load side neutral terminal. This current flowing back will then cancel the magnetic field within the CT of the GFCI that's being caused by the appliance leakage current I
L. Therefore, if the appliance is plugged in then the GFCI should be able to be reset due to this opposing current flow. An 0.1 μF capacitor would draw about 4.5 mA with 120V across it, so that could be a starting point and then varied if desired.
This would only be a test to confirm that a capacitive current of a known amount is causing the tripping. It would definitely not be an acceptable fix for a problem inside of the appliance, because it's effectively biasing the trigger region of the GFCI off from 0 mA.
I realize that digging this deep into the problem may not be ultimately necessary to bring closure to the OP's situation, but I think it could at least provide an opportunity to get some insight into what's going on.