David King can build a sweet bass, but I don't think he does refinishing.
Call Five Star Guitars. There is a guy that they sometimes farm stuff out to named Brian. He also builds basses, and there's a Jazz bass there (or was) that played way WAY better than any off-the-shelf J. It also had a beautiful burst finish that he did.
Anyway, they might call him and have him call you. Good luck!