sponsor a J1 Visa.
The J1 visa program will cease to exist fairly soon:
AOPA Online: Work-study visas for flight students set to end
so you're saying that it's easier to get a JAA medical class 1 if you allready hold a CPL
Yes, it is. I don't have the song and verse in front of me know but a holder of an ICAO CPL has different requirements for the JAA Class 1 medical.
If you are looking at a school with a J-1 program have a look at NAIA:
NAIA- Flight Training for Pilots - Aviation/Flight School
Have heard nothing but good things about them.