From the thermostats circuits I have seen a snubber is not used. I experimented with many snubber designs to minimize relay arc and few showed any promise. From what I read the GFCI's work by sensing a imbalance between hot and neutral. I wonder if the relay arc is enough to upset that. The surge protector may not be the answer but something easy enough to test. I am not sure if it would provide any filtering or not. Line filter is a good solution but will also be costly. Zero crossing has worked the best in my testing and while a mechanical relay timing is not perfect you can still greatly minimize spark and I suspect much less likely to trip the gfci.