Once you have your FAA Multi/CPL/IR then it's a straight license conversion... ie ATPL writtens, CPL - training as required, IR - 15hr conversion course of which 10hrs can be in a sim.
Also, as long as you hold a FAA class 1 medical, then your JAR Class 1 doesn't have to be an initial, it's just an extended renewal. That means for example, if you have any minor eye sight issues that would preclude a pass at initial but are within the limits for renewal, then you can get it issued.
All this is well and good as long as you're on top of your game and get through in minimum time... if not it could wind up being a nightmare!
Other thing is not many schools in USA will teach you anything to do with an NDB due to the fact that they are considered mostly obsolete there... Might make for a rather rude shock when you arrive with a fresh FAA IR expecting to pass in minimum time and now you have to learn single engine NDB holds/approaches on top of all the other operational differences. (It's not magic though!)
If you find a good school with a good instructor and you put the effort in then you should be fine taking this route.