Strange results from my testing:
Anytime I plug in the heater, it trips the GFI. I tried plugging in to another GFI circuit, and it does the same thing.
The replacement heater and cord came in today. Hoping it was just the cord, I plugged the new cord into the old heater on the engine. Same results: tripped the GFI.
Just as a test, I plugged the new cord and the new heater (not mounted on the tractor) in to the outlet. The heater operated normally.
These tests indicate a problem with the heater itself. Out of curiosity, I checked the resistance of the new heater, and compared it to the old. I could not measure any significant difference. It's odd. I expected to be able to see some difference that would cause the GFI to trip. It was a cheap Harbor Freight ohmmeter, so maybe it was not sensitive enough. Or maybe the few volts put out by the ohmmeter are not making it through like the 110VAC would.
So I guess replacing the block heater is in my future. I had hoped not to have to drain the coolant (I have no heated work space for this).