2000DX
Having seen a colleague with this problem, trying to fly N reg from the UK into Europe, the problem you face is that your national licence [non faa] is not valid outside its own country because you are then in INTERNATIONAL airsapce, and thats where you fall foul of not only the FAR`S but EASA rules, or for that matter ICAO rules.
The best way is to get a stand alone FAA licence, its so easy!.