Conversion as such may not be needed here.
There is no reason why a particular training flight cannot count towards more than one license/rating.
For example, you could do a dual flight with an instructor (JAA instructor, G-reg plane perhaps) and that one flight, if over 250nm, at night, IFR, under ATS direction, ending with two T&Gs and one landing (all 3 IAPs being of a different type) will be good for
1. FAA PPL night requirement
2. FAA IR x/c requirement
3. JAA PPL renewal
4. JAA IMCR renewal
and probably a few other things to do with night currency. All at the same time, on the same flight!
There are issues with instructor ratings; in the above example he would need to be a JAA instructor as well as an FAA CFII.
I've been offered the above by a few people in the USA, for doing the FAA standalone PPL and the FAA IR both at the same time. (Obviously this is workable only if the pilot already has instrument skills under say a UK license; a first time PPL could not usefully absorb the IR training).
So there is no reason why a student could not come out with both a JAA PPL and an FAA PPL at the same time. The training for the two is slightly different (extra stuff in the FAA PPL, including extra instrument navigation, and the night qualification is mandatory under FAA) but it could be combined easily enough.
What one cannot do,
AFAIK, is train for the IMCR and the JAA IR at the same time (i.e. after the 15hrs decide one doesn't really want to do the IR, and settle for the IMCR instead, or after 15hrs decide to continue to the full IR).