You can't do a JAA IR in the USA. You may be able to do training towards it with a JAA approved FTO but you will need to do the test with a JAA examiner. Flight with an FAA Instructor does not count unless you do the whole ICAO IR and then convert it later.
If you are returning to the UK for the test it will have to be with a UK CAA examiner. It is possible to do the flight test in another JAA country and have the paperwork processed by the UK CAA. They don't like it but they do it.
There is also a quirk around where you do the theory element in relation to the flight training, but I am at work and don't have the reference handy.