Hi @jea48 - Not my first time going through a balanced power system, though it is the first time I've known about GFCI on an example. I read through your explanation, which is what I remember. The part that I don't get is how a GFCI, connected to the secondary windings, tripping on a balanced power system would not also trip the kitchen outlet.
As you point out, the ground is not part of the GFCI sensing strategy in either case, but it's the imbalance between the current carrying conductors (which ground should not be except on a fault) which causes the trip.