Aw Poo...Geoffers.....I am not up on border crossing now days....but it poses an interesting scenario. Dutch machine, British pilot, entering the US and then leaving again across the country.
If you flight plan the shortest route (usually not the most scenic how ever)....and it shows entering the USA which I am pretty sure it will....I bet it will not be a major problem....but advance contact with the FAA FSDO in the area where you wish to enter might be advised as well as ensuring you have the correct paperwork for the Customs guys.
I promise you this....you better have a load manifest (US Customs version) ready when you land in the USA....no sense of humour those guys. They can assess you a 1000 USD penalty on the spot....but only notify you by mail months later.