Got a free Wednesday?
Take an early ferry on Saturday over to Cruz Bay and go over with Low Key.
Low Key Watersports - Diving in St. John, US Virgin Islands
No one - that I know of - does it from St. Thomas any longer. Sawyer's in the East End (now Red Hook Dive) used to but RHD doesn't.
Since you're temporarily there, maybe pop over to Roadtown (Tortola) on the ferry and find someone who'll run over there. bviscuba.org lists all 8 possibilities.
Check with DiveBVI - the ferry to the Virgin Gorda Yacht Harbor docks about 200 yds. from their dock. We dove it mid-week with them but we also flew out Sat. morning. Afaik they dive every day - certainly on Sunday with us. It's about the same run for them as it is from Roadtown for the Tortola shops so it's a possibility.