U.S. Company with EU Pilot Domicile?
I've barked up this tree before (I've got German citizenship, work rights, and speak the language, but don't have a JAA). I've only found 2 possibilities: 1. Find a wealthy American who has moved there, or 2: try and find a company with a base there (like you said, FedEx). The problem with two is finding a company where that would be a junior base! I know this doesn't really give an answer you want, but without a JAA, it's rather difficult to make the jump.
Good luck and if you find something, please share!