I've just been talking to the FAA about this one. I spoke to a very nice operations inspector chap at the New York field office (001 718 553 0986) and asked how I stood as a non-US citizen holding an FAA ATP with regard to hiring an aircraft. Absolutely no problem, he said, there are no extra measures in place, all I have to do is a check ride. So there we go. Next stop the travel agents.