The JAA program at Bristows Academy is fully booked until January 2011. So unless you want to wait a long time, the FAA route is the only option. It's always better to get more hours and experience and working as a CFI in the US is good experience. (but it's not a walk in the park)
After you finished the FAA ratings, you should consider starting the ATPL theory, if you do this with Caledonian (CAPTonline) you can do the refresher weeks in Florida (at Bristow). After the exams you can do the CPL(H) flying and exams with Bristows and basically you have the same as doing the Bristows JAA integrated. Also the cost wouldn't be much higher.
The J1 visa will end, but there will be a change to the M1 visa program with basically the same options, so no need to worry there.