We need to clarify the situation in regard to obtaining entry.
For an enlisted man, say airman aircrew, the requirement is that you must have permanent residency, not an easy thing to obtain. But if you have that, depending on the USA requirements, you can enlist provided you enter into an agreement that you will become a US citizen as soon as the waiting time was up. This period used to be 2 years.
For officers I am not so sure, I have only had contact with one USAF Captain who was originally an Australian, but his mother married an Americian and he went to school and university over there, and I guess along the way he gained citizenship.
Whilst in Vietnam, I met a T/SGT C130 loadmaster who held Scottish nationality, but told me that when they looked like putting the hard word on him to change, he was going home. He had been a member of the RAF, but when he enlisted in the USAF was a civilian.
I think you will find that exchange duty is no big deal, to to move over into USA services, may not be easy.
Regards
Col Tigwell