I don't know how quick of an upgrade you're going to see at your 737 or 320 operation over there, but you'll need to sit as a Captain for a while before the American majors will even consider you. 1000 hours Turbine PIC seems to be the magic number. PICUS time is a European invention, and the U.S. carriers won't consider it the same way that they do over there. And yes, you're certainly going to need that 4-year degree. The other sad truth is that unless you're female, you'll need help from current pilots for internal recommendations. That said, time on either of those aircraft might get you attention when you try for the American majors, as your main competition will be from RJ and military pilots. The other issue you should consider is whether you would really want to change over to the US after you've landed a job flying that kind of equipment in Europe. I'm sure you're familiar with the level of morale at the American majors...