"I found a 2nd GFCI outlet in my house which was hiding behind boxes about 3 ft. high on my garage rear wall."
I would have bet you lunch on this one...
Great! Cheap fix so you had a couple of bucks for the HVAC dude.
Since the GFCI has to be the first in line on the circuit, it is usually the one closest to the breaker box.
And the $200 was easy to spend, wasn't it?
You should be able to squeeze a few more years out of the heat pump, I would think.