Weather it's car repairs, or home repairs, always check the simplest things first

I wish to heck you'd asked on here before you started throwing money at parts. I used to maintain/ repair/ install HVAC. Unless things have changed, a dedicated circuit for a permanent heating/ cooling appliance does not need GFC They are "permanent" and are supposed to be additionally grounded. If nat gas, then the gas piping is supposed to be bonded to a ground. (The meter is isolated by dielectric joints same as a water heater)

Yeah, I wish I had too, maybe someone would have told me to check power first. Anyway, live and learn. Just glad it's up and running.
I added the furnace later after the rest of the garage was done. I don't think it was my intent to GFI protect the furnace. But I had a breaker that only had one outlet on it, so I tapped into that for the furnace rather than adding another breaker. Never caused a problem till now. I could add a breaker and re route the wire for the furnace if you think there is any kind of safety issue with having an outlet and furnace on the same breaker.