OK here's the scoop on doing it. First Find a School. Sierra Academy of Aeronautics offers work visas for instructors. However, you should get an M-1 to start with. Here's why:
You cannot "convert" a JAA CPL to an FAA one. The FAA will give you a private with the class ratings you hold on your JAA CPL (Single or Multi engine land).
If you have your IR, you take a written test and get IR privledges on your converted license. If you do not have an IR, you must obtain one in the US. You cannot instruct in the US without an IR.
Next, you must do some training in a complex aircraft (Cutlass, Arrow etc) and take the practical test for Commercial-pilot ASEL. Requirements to take this test are 250TT, 50 PIC Cross Country (Greater than 50NM), 10 hours in a complex aircraft.1 written exam, 100 multi-choice questions.
Once you pass this, you do the same in the twin and add multi-engine class to your commercial.
Next you embark on the CFI, which when passed allows you to teach Single engine VFR ratings. CFII allows instrument, MEI twin instruction. After getting all this muck, apply to Sierra or a school that gives a visa and have them issue you a J-1.
The only snag you may hit is a lot of places have FN CFIs that work for free for the time, and wont sponsor a J-1. Best of luck in your quest mate.