Hi Fitz - good for you for wanting to abide by the rules.
Good news, bad news. The BVI/USVI boundary is routinely crossed by vessels underway just transiting the narrow passage
around the west end of Tortola/Thatch Island and the north side of St. John. I expect you could circumnavigate St. John without clearing in and easily get away with it, although around the west end where custom/immigration is available in Cruz Bay you'd have a difficult time explaining why you didn't. In my many years down there I've never seen or heard of a foreign cruising yacht being "pulled over" while underway to be questioned. Neither the USVI nor the BVI has the personnel resources to do that. That's the good news. The bad news is that it'll be obvious that your charter boat is from the BVI. There are only a few charter companies in the USVI and they are not the same companies as in the BVI. Your Sunsail/Moorings/Horizon/Voyage/whatever BVI charter will stick out like a sore thumb. Everyone will know you came from the BVI side. Whatever you do, do NOT hoist a US courtesy flag to pretend you cleared in. If anything, fly a Q flag showing your intention to clear in, then change your mind and do not stop.
But why bother? St. John is fabulous and there's nothing you'll see to put you off except maybe the Coral
Bay area. It's a crowded anchorage with a lot of worn out liveaboards. Most of the rest of the island is US National Park with mooring required anchorages
that rival anything in the BVI except they're free of beach bars. Moorings are $15/night vs $25 or $30 in the BVI. AND - there's very few charter boats.
As a compromise, while transiting from Jost Van Dyke through Thatch Island Cut into Drake Channel (or vice versa) take a short detour in and out of Leinster Bay or Francis Bay on the north side of St. John and have a look. If you somehow get "pulled over", just claim you thought you were in Cane Garden Bay. Being a charter boat, the authorities will certainly believe you were confused...