You can fly G reg ME aircraft on an FAA certificate as already stated. I think to get issued a JAA ME rating directly depends upon number of hours you have in a ME aircraft (may even be PIC hours). You are excempt from the 6 hr course, and just need to do the flight test otherwise.
However, before the FAA IR can jump into any seat of authority in a Boeing and fly to London, he needs to pass an ATP flight test
Theoretically an FAA CPL / IR could RHS....
The Ground Exams are much easier, and the Practical Test standards permit lower levels of accuracy (ILS needle deviations for example)
Mind you you have to be better at partial panel stuff. the FAA expect a non precision approach to be completed partial panel, whereas JAR only require partial panel basic instrument flying .....but you already knew that