I did my FAA ATP, based on my JAA ATP together with my type rating.
Since you've only the FAA PPL, you will need to verify your JAA Licence with the FAA Verification Branch, then doing the written test and the checkride in the Simulator.
Verification takes around 2months, depending on your CAA. Mine screwed it up the first time and i managed it the second time after 3months. The verification of the FAA is the valid for 180days.
I also had to show up at the FSDO with my logbook, as they needed to check if my flighttime fulfills the FAA requirements.
Good luck