You may be missing the point slightly.
For the time being the regulators don't care where a crew lives, where they are based or who they pay their taxes to.
What they do care about is the location of the operator who they work for.
The case of UPS, Fedex, AA etc, these operators are the other side if the Atlantic, their pay checks come from the other side of the Atlantic. It's irrelevant.
However, if you fly a CJ or even a King Air on a non EU reg and the operator is based within the EU and you fly within European Airspace. Then you face a problem.