I feel like it makes no sense to try to stay in the BVI on the 2nd. It will just make your trip home on the 3rd that much more stressful/complicated.
Your timing is very lucky though! Interisland Boat services runs a ferry from Jost on Tuesdays back to USVI! It leaves at 3:30 and routes through St John, ending in Redhook.
Leaving the BVI on the 3rd just gives you more hoops to jump through.
You could consider staying in St John and not continuing on to STT that same day, although your options for one night are probably limited and pricey. Plus, you would have to be on the 11 or 11:15 outta there the next day so really, what is the point?
Since that ferry would take you right into RedHook I personally would probably lean to Sapphire Beach or Secret Harbor if they would accept only one night. Then all you deal with on departure day is a taxi to the airport. Since your flight is so late there should be no reason to try to get a place super close to the airport (like Emerald).