There's one other thing to check. One of the entry requirements for an FAA CPL is an ICAO PPL, but I don't know whether that ICAO PPL needs to be valid at the time you do the FAA CPL exam, or whether an expired PPL would also be sufficient.
And also, you need to have JAR medical.
I think, but I'm not quite sure, that the medical is an exception. You can fly an FAA piggyback PPL on a medical that goes with the underlying "based on" licence (in this case a JAR-FCL medical) or on an FAA medical class III. So for your FAA piggyback PPL to be valid, you don't have to have a JAR-FCL medical per se, as long as you have an FAA medical. But it's something to check out.
However if the underlying JAR-FCL licence is invalid, or if the class rating is invalid, or something like that, then the FAA piggyback PPL is also no longer valid. That's the problem with these piggyback licences: You're building a house of cards, and all it takes is the removal (expiry) of one bit, and the whole house will come tumbling down. An FAA piggyback is great for the occasional holiday touring, but if you're going to do more flying than just that, for a more extended period of time, it's better to get a standalone FAA PPL.