"If you have the right to live and work in the EU (sounds like you don't) then it is possible to get on with a European airline with a one year validation. In that year it would be up to you to take all the required JAA written exams".
The likelyhood of being hired by a European Airline without a JAR license is very slim indeed.
Waivers have been issued before because of pilot shortages but it's uncommon.
Attempting to pass all 14 JAR ATPL written exams inside of a year is a tall order even if you hold an FAA ATP. There's a lot of material in there that's not covered by the FAA.
Good luck.
AL