We normally go through San Juan, but according to CPB, there is no Global Entry at STT. As Malcolm said, your plan is fraught with potential issues.

Spending the night at Norman (not Normans or Coopers, btw) puts you closer to Sopers, but doesn't really solve the other issues. The usual advice is take the 7 am ferry to make a 1:30 pm flight, especially on Saturday. Why risk ruining a lovely vacation by missing your flight home, especially when planes are operating full?

Can you change your flight to Tortola? There are later connecting flights in San Juan than from STT.

I know you have booked at Scrub, but another day on VG would be more enjoyable, in my opinion.