Wind Star yatchs have some itineraries out of St. Martin that have overnight stays in some of the BVI ports. I don't know if they dock there so you can easily come and go or whether they just drop anchor in some beautiful cove.
A Bad Day At Sea [with power] Always Beats A Good Day At Work
Carnival: Glory 2004, Destiny 2008, Splendor 2009, Freedom 2011, Valor 2012, Dream 2013
Celebrity: Summit 2011
Princess: Ruby 2010, 2014, Caribbean 2013, Coral 2014, Regal 2014