my 2 cents
Right, I hope this clears something up. In order to work in Europe you have to have your JAA stuff. It is more expensive though, so what lots of people do is come to the states, get their FAA stuff, instruct to build some time and then convert their FAA ( US) stuff into JAA stuff, which is not that simple. I have my FAA ATP, with more than 1500 hours but I still have to do the JAA ATPL written exams, a commercial JAA flight check and 15 hours min IR course to get the JAA IR. I know phoniex east pretty well, as I worked for the big flight school next to it and have a relative working there. Its got pretty good rates, but you get nearly all that flight time, 1500 hours of it from instructing. And you will have to get it done before your visa runs out etc. After you do what I am doing and sit the groundschool, 6 months and then the conversions.It gets complcated, and flight schools tell you what you want to hear, so get some good advice before decieding what to do.
I dont know the specifics of your situation, but if I was you I would come to the states, and get my FAA private certificate. With thi in hand I would sit the groundschools for the atpl, then I would finish my training in the states and build some time intructing and do the flight conversions when I got the chance, that way you could aplly for work in europe while you were instructing tin the states. Hope this helps, and good luck