Today I hosted a workshop with Shawn Knudson, the Vista rep in Oregon, and during the discussion, this very topic came up. He said electricians will always blame the GFCI but it may be that the transformer is creating such a large inrush of current that the GFCI naturally trips off.
His recommendation is to try running a temporary extension cord to the transformer from a receptacle and circuit that is farther away from the transformer. If that circuit breaker trips off when the transformer activates, it's a safe bet that the transformer is suspect. If not, it may be the GFCI is weak. He also suggested that one should use a, I believe he said, a MAC Breaker. A heavy-duty product that you will not find at HD or Lowes, so may have to go to an electrical supply store.
Hope this helps.