I went to Soper's Hole earlier today and checked out all the boats - no luck there, either.

Yacht theft is relatively rare in the Caribbean - it is hard to escape when your getaway vehicle moves at less than 7 knots and there aren't as many havens as one would expect. The French Islands are a likely destination immediately after theft since they do not require outbound clearance to make a yacht "legal" with inbound clearance.

Have you contacted https://safetyandsecuritynet.org ?