If you charter out of St Thomas (CYAO for example) you can leave direct out of Charlotte Amalie, stop by St. john, check out and then head to JVD to check -in to the BVI. The better flights and convenience of flying in to STT instead of flying STT and ferrying over to Rd Town or flying into Tortola may make up for less selection in St Tomas. Never used them but CYAO seems like a quality outfit.

All that too say definitely doable! Might do that next trip to USVI/BVIs.