I just had a frozen ATPL (CPL/IR) JAA and did my FAA ATP based on that. Just do the FAA ATP written ( I did mine at FS in Paris) then do your ATP checkride with your type rating.
You do not need a ride in the aircraft for FAA type rating, level D sim is Ok. You do need additionally six take off and landings for the JAA rating.
I have both and my first jet rating was combined with my FAA ATP checkride in the sim.
I did all mine at Simuflite in Dubai, very well organised, very helpful.