Not sure why you are looking at FAA ATP and JAA training?? It is also very interesting about the CAA wanting a PPL to issue a Class 1 on deviation - can I ask why? Does the PPL have to be a JAA PPL as you can start the JAA ATP written exams with an FAA PPL and in fact never get a CAA PPL.
To clear a few things up. You can convert an FAA PPL to a CAA PPL by doing two written exams and a RT test and Flight test if you have more than 100 hours TT, in my mind, you might as well do the other writtens!
To do ANY flight training in the US you need a student Visa ie M1 or J1 and you can therefore only go to a school that can offer an I-20. Not all courses need TSA though - I don't think CPL does! see
www.flightschoolcandidates.gov
Look at what licence you really need - the US can cost you more in the long run with TSA, travel etc and more training than you expect on return home. If you need an FAA ATP, then forget about the JAA at present and concentrate on the FAA route with a J1 visa. I would also look into how the EASA might affect your class 1 deviation when they take over flight crew licensing in 2009.
All the best mate