Firstly your posting in the wrong forum - Flying Instructors and Examiners forum is where you want to be - where the question was recently answered.
Have you looked in LASORS?!?
You will still have to sit the CPL exams - which can only be done in the UK.
The ATPL exams which would cover the IR can be sat in the US.
FAA licences would be valid on N-Reg aircraft but not G-Reg aircraft - may as well just train the JAA stuff in the first place - it'll be cheaper in the end.
Conversion wise to JAA :
CPL (Can be completed in the US)
Can be converted training as required. (Can be completed in the US) Word of warning, no necessarily cheaper or easy - I have seen many students struggle FAA > JAA CPL.
FI (Can be completed in the US)
Pretty much a 15 hour course to convert plus relevant groundschool.
The JAA FI is more in depth - rather than the training as required (3 minimum) for the FAA CFI.
Good luck.