Once you hold a JAA ATP or a US Commercial (which you said you have) than you can just come over here and take the ATP Written and ATP checkride. Piece of cake. If you did this in a small twin engine piston at a place like ALL ATPS than you would save alot of money.
I'm not sure if the type ratings on your JAA ATP would transfer to the FAA certificate though. Have you tried contacting flight safety or simcom to see what they have to offer. I have heard of programs for FO's to get type ratings without buying a full course.
Not sure if they have this for the 737 though.
Good Luck and let us know what you find out.