That's weird on the GFI, our problem with the floor heat was a little different. They would come on but not stay on, going off after a few minutes, turns out it was a software fix that needed to be done, but yours sounds a little different. It is strange that they would have them wired to a GFI, but it does seem that they make each unit just a little bit different, good luck and stay warm.
David & Anne Marie
2015 Dutch Star 4369
All Electric Coach
HWH Active Air Suspension 2014 Wrangler