Couple more points. You do NOT need an FAA medical to fly on a piggy back license. The license remains valid subject to your JAA PPL remaining valid, and your JAA PPL requires a JAA medical in order to exercise.
Legally you do NOT need a BFR. This has been recently confirmed by the FAA. The currency of the based-on license (ie. your 2-yearly SEP renewal) is sufficient to exercise the privileges of the FAA license. That said, you almost certainly won't be able to hire a plane in the USA without evidence of a BFR.
Here's a handy article I knocked up a while back regarding getting a piggy-back license (all info current and correct):
http://flyerwiki.netsplit.com/wiki/F...y-Back_License