As one who made the move from Europe to the US a few years ago I can tell you to stay where you are and try to work it out with your girlfriend. I already had the FAA (and JAA) license so that was no issue for me. The grass is far from greener over here, especially if you're a pilot.
I have pretty much realized that I belong in Europe and that the life as a pilot is usually much better over there. The T&C's offered in the US are in most cases laughable. First good chance I get I will pack the bags and head back east.