I swapped the GFCI breaker with another GFCI breaker. Same behavior. It trips.
Connected a real grounded load (500W work light) to an outlet at the end of the circuit to test everything up to just before the heater. Worked fine.
I didn't understand why the breaker would trip if I had a switch on the hot line side turned to OFF. There should be no current flow to measure, right? So, just for testing purposes, I removed the ground from the switch temporarily (but the heater is still grounded back to the service panel). The breaker stayed on this time until I toggled the switch to ON. The heater fan just barely started then the breaker did its job and tripped.
@Paignton pete are you suggesting that since the neutrals and grounds are all bonded together at the service panel, if there is a ground fault in another circuit in my home, it could actually cause the GFCI breaker on the heater circuit to trip? I have numerous GFCI outlets on various circuits that behave OK currently, but no other GFCI breakers. Pardon my ignorance.
It seems, as
@littlespark has suspected, there is a ground fault in the heater unit. I will contact the manufacturer to see if they are of any help. Is it possible that I'm not going to have any success using a GFCI breaker with the heater? That there is some innate characteristic of the wiring of the heater that it will always show a ground fault (albeit perhaps a "minor" one that is registered by the sensitive GFCI)? Or is this a bonified appliance defect? My now frustrated instinct is to just remove GFCI protection from the circuit, but that doesn't seem right. Or would it be just fine under normal use to not have GFCI protection? I'm sure the majority of these heaters are installed without GFCI protection and I don't see that the NEC requires it. Though I do work with building codes (structural engineer), so understand "code minimum" vs best practice.
See attached (2) photos of my service panel and the (2) GFCI breakers. The lower of the (2) breakers is the one in question. Hard to see with the long breaker bodies and pigtails in the way, but the neutrals are in fact attached to the breaker, then the pigtail to the bus bar.
Side question: I had this panel replaced a year ago by a professional (and the City inspected it). The electrician ran all the cables through a single large knockout (top right of photo) and removed the screw down portion of the cable clamp (but at least leaves a grommet of sorts). The cables are not attached to the wall framing except with a "lasso" of NM-B insulation sheath. The bundled length is less than 24" from top of panel to wall top plate after which they fan out somewhat. From what I can tell from reading the NEC, it seems only (9) current carrying conductors are allowed through a knockout, no matter the diameter and the cables should be clamped within 8" of the knockout. Is any/all of this not code compliant? Maybe the City was lenient in this case since they were removing an old Zinsco-Sylvania panel which are known to be fire hazards, thereby at least mitigating a known hazard.
Thanks again, all.