You may have to get your medical before going out.
Technically you may possibly be able to get your JAA medical in the US. But if you don't qualify for a medical, the whole endeavour is a waste of time and money. So before you commit ANY funds in this undertaking, make sure you qualify for a JAA class II medical - by getting one.
Also you have seen this thread, haven't you:
http://www.pprune.org/forums/showthread.php?t=278995