Provo,
I have just done a greater than 12500, actually a 28450 type rating, on a FAA license I got pre 9 11, and did not have a visa on a British passport, I was told I did not need one by the TSA (visa sect) and by the training facility.
I am back at home with type rating and ATP in hand, with no problems at all, I was honest and up front with IMM. Official and showed him the TSA paperwork. Just have everything (paperwork) in order and available.
PM if I can assist.