Eagle737
I guess that the first problem would be the work permit/permanent resident visa (both in Europe and USA). Before you start investing any money towards your JAA or FAA certificate this would be your first obstacle to tacle. Even you would have a valid pilot cert it will most probably be virtually impossible to find a job without the work permit.
What comes into the pilot certificate, I do believe that only the authorities will be able to tell what are those actual training courses & tests you have to take before they can issue you a valid lisence. I would suggest that after you have aquired the work permit into the country you want to reside, just contact the authorities and ask for their advice. Make sure that you will have all available copies of your initial and conversion training, including all check rides, as well as full records of all your flying experience.
As about your type rating in 737, I'd guess that it depends greatly where you actually did your rating course, if it was done with some well known training school (like Boeing Flight Safety, in Seattle) it shouldn't be too difficult to get it accepted afterwards by the authorities. But if not, oh boy, I wish you the best of the luck...
One thing is for sure, it will take some time and a quite big economical investment to complete your plan, but I guess if there is the will there's the way...
I'll keep my thumbs up, and wish you the best of luck in the future!!!
///Aviate