B2 - long final is not looking for a licence, he/she is looking to exercise the priviliges of a rating.
What, in the current FAR's, prevents him/her taking the IFP (Instrument Foreign Pilot) written examination in order to exercise the privilidges of his/her foreign (in this case, JAA) instrument rating on his/her current FAA CPL?
Things may well have changed since 9/11 - but it's what I did when I first arrived in the USA. A stand along, "US Test Passed" flight test for CPL with IFP privilidges.