Island Time or Chillout Water Taxi. Used them both BVI to Red Hook. I would hesitate using Dolphin as they have struggled this last year, according to comments I've seen here on TTOL and elsewhere.
What Husker said. I also imagine both would be able to pick you up from St. John directly.
If you would rather use someone based in the USVI I recommend Midnight Sun Charters. They have 2 beautiful Midnight Express boats