FAA to JAA conversion takes more effort than you might think. But it can be done quite quickly (weeks), the theoretical exams at a US flightschool.
In the end I would ask you to reconsider. I have been there, and done that. You can't take your 401k to Norway. You might have to pay norwegian taxes on your A/B Fund (Norway-US tax agreements). You'll pay 2-3 times more for gasoline. Food and clothes is more expensive. I can go on...
I know a number of americans here that would agree with me.
Your lifestyle at Norwegian would be substantially lower than at Alaska Airlines.
But if you have to ,you have to...