Owning a boat in the BVI surley must be a good reason for them to extend/issue your visa.
I've had a boat in the BVI for several years and it is a real pain to make the trip to Road Town to get the 30 day extension. It will generally cost you several days hassle and to me definitely NOT worth it. It is even more difficult to get the 2nd extension and it is typically given for emergencies such as medical or boat repairs not completed and you have to have full documentation on either.
Like almost everyone I know... I also head over the USVI for a day or so. I actually typically go for at least a week because I love to sail and hike around St. John.
HOWEVER, you have a PROBLEM... your British. Due to some Tit for Tat rules based on what private US boats are required to do in UK, the US adopted the same rules for UK boats in the Carib. You have a problem entering the USVI on a private boat with out advance approval. You may come by ferry boat with no problem but then you will need to stay overnight.
You can get the advanced approval if you apply. I have several Friends from Wales that recently did that so we could sail in on my boat when we wanted to hike and visit the big stores in USVI. Not sure of the form name but I'm sure you could locate it.
Do note that if you have a 30 day entrance permit and leave prior to the end and return prior to the end... your next entrance visa will be ONLY for the remaining days. Do Not return until after the initial 30 entrance permit has expired.
Funny how governments forget about little cruisers and make life difficult to go a mile and a half.