You also need an FAA license validation, as you can't just fly an N-reg aircraft on a JAA license.
Info here:
Airmen Certification: Verify the Authenticity of a Foreign License, Rating, or Medical Certification
If all you want is to fly over the GC, it's probably best if you simply hire an aircraft and an instructor.
There's a recent thread on here about this very subject (flying the GC from Vegas on a JAA PPL) - search the archives.