If I were you, I'd try to get hired at a regional in the US, and simultaneously work on the 14 exams via distance learning. It will take you longer to finish the exams, but you will get a type rating and lots of time on type. Once you get your FAA ATP, and your JAA exams are finished, you could convert the license on a simulator that you are typed on (with 500+ hrs on type)
It really sounds like you are ready to move beyond the instructor stage, do you really want to be bonded for two more years of instructing? Sure, a regional is low pay and lots of work, but the European carriers seem to value jet time quite a bit. Plus, the way the US economy is going, who knows how much longer they will be hiring... Same goes for the European economy... After your two years of being bonded, the little bit of hiring that is happening right now may not be happening at all anymore. It is too hard to predict. So, worst case scenario, a two year instructor bond could turn out to be a much longer instructor stint. Maybe being a career instructor turns out to be what you want, but currently it is not in your stated goals.
Just my two cents