I see no reason why you would not do all of your licenses abroad followed by conversions back in Europe.
Even if you can't do a straight conversion, some additional training time plus a skill-test will still save you a tremendous amount of money.
Spend some time finding a couple of good schools in the US/Canada, do all your ratings up to FI, work for a year and go back to Europe with a 1000+hrs ATPL exams and conversions and now you're a 1000 hr pilot looking for a job competing with 300 hr pilots.