Yes, as BP says above, you need a trust. Several hundred UK pilots use
this firm which offers reasonable value for money.
No idea on import duties or other taxes in the DR. I would ask another foreign-reg pilot you see hanging around and find out what he did. I dare say paying off some official is the standard way things are done down there
The world is full of N-reg planes... only a few countries ban long term foreign reg parking outright.