Ahoy Captain,

You may want to consider a Red Eye through Toronto, a morning flight to SXM, and then hack an afternoon flight on Winair to the BVI (EIS)
You may want to consider a short overnight at FLL.
FLL has many hotels close to the airport under $100 Night with a free airport shuttle.
FLL has discount Airlines that now fly to SJU and STT.
FLL has several early flights to SJU with connecting midday flights to EIS.

Fair Winds, Brent from The Captains Compass