Fyi Vpb Vpc
In order to operate the a/c in the European theater or elsewhere in the world, with no ramifications , you will have to set up an account in either Bermuda VP-B** or Cayman Islands VP-C**. The aircraft can either be USA or Europe owned and operated , either Private flight (Part 91) or for hire ( Part 135). Tag Aviation UK & CH and Jet Aviation CH both operate a fleet of aircraft that way and successfully for their respective owners. I have flown on either side of the Atlantic on VPB and VPC aircraft. For the crew it means that doing you annual simulator session and then send your paperwork of to the respective authorities. The airplane has an annual "paper" inspection with dedicated OI assigned by those countries, next to it's normal FAA/JAA etc country compliances. And it is the extra costs that make it sometimes prohibitive, but you do get that cool call sign.
For a single individual to achieve all this is very time consuming and frustrating as the information is out there but it takes a very long time to get all the ducks in a row and then keep them in a row. Hence a management company, with considerable experience in that field is a clear winning proposition.
I have no experience with M registered a/c.
Good luck