Do you have or can you get the legal right to work in the US? If you can forget about the EASA stuff for now just concentrate on getting the FAA CPL/IR Multi. You would have to be very lucky to get a job in an airline in Europe with a fresh FATPL and even luckier to get a job flying a light aircraft if you don't get straight into an airline.
If you can legally work in the US you would be unlucky to not be able to find a paid, albeit low pay, job in a light aircraft. Thats if your willing to go anywhere in the states to work. The opposite is true in Europe. Once you have your FAA CPL/IR and have found a job start studying for the EASA ATPL ground exams, unfortunately your FAA knowledge will do little to help you with these exams. You can build time whilst studying and bit by bit convert the rest when you are able, CPL, IR etc, if you decide you really want to work in Europe.
In the states I could almost guarantee that with motivation and drive you would have some jet or turboprop time within 3-5 years. In Europe I could almost guarantee you will not have found a job within 3-5 years.
If you find the right school with nice weather you could be qualified within 6 months and looking for that 1st job.
If you can't work in the states, good luck.