I would suggest you use your FAA licence and if possible stay in the US and instruct. Build your experience and keep your licences current.
Don't get in to a position where your FAA licences have expired and you can't get a job with your JAA licence. Of course you can renew your FAA ratings in Europe and maybe you can fly N reg aircraft somewhere.
Do not pay for a type rating. Not unless you have an absolutely guaranteed job offer. There are literally hundreds, if not thousands, of very experienced pilots on the market the world over who have thousands of hours of airline experience and who are now seeking work. Against them you have no chance.
Save as much money as you can. Do your JAA fATPL as slowly as you can while keeping your existing ratings current. Maybe the market will improve in a couple of years as long as fuel doesn't go sky high again. I suspect it will as a lot of hedge funds made an awful lot of money the last time it went up.
Save your money. Keep current.
Good luck