Answer this question,
As an EASA or then JAR CPL or ATPL licence holder can you go to the USA and domicile yourself with a foreign registered (read European register) and fly/work in the USA getting paid for your services ? regardless of private or commercial operations, you are paid as a pilot.
I think you know the answer, that is what I believe is the one of the main reasons for the EASA proposals to protect the working rights of the European pilots, the same reason why you cannot do the above scenario.