One more thing regarding FAA PPL.....not sure why you want to 'de-restrict' the FAA PPL, unless you're going to let your JAA one lapse. A 'restricted' FAA PPL is as good as a de-restricted one, the only difference being that your ratings from the JAA PPL are carried over to the FAA one. The FAA PPL allows a pilot to fly at night as part of the training is carried out at night, but if you have a JAA PPL but no night rating, your FAA PPL won't allow you to fly at night.
You can build onto a 'restricted' PPL, for example do the FAA IR then your FAA PPL is marked as 'test passed'. Like Noggin said, if you want to derestrict your PPL then you have to do the ground exams and flight test. One interesting thing though, if you carry out further training in the USA, eg do an FAA CPL then this superceeds the PPL and you will be issued a 'proper' CPL with out having to do the PPL exams and flight test.
Another point, if you do your JAA licence in the states and pass, you cannot get a FAA PPL until you have your JAA licence in your hand (ie CAA have processed it)....well you can get it but should you get ramp checked, you have to produce you JAA PPL as well and if you haven't got it, and you're still flying on a student permit with passengers, you're screwed!