It's a long slog to Anegada from Tortola, been there, done that. Better off going to Anegada from North Sound or even Trellis, both much easier sails.
Renting a car from Speedy's is super easy from Leverick, they spot the car there for you and you stop by their office on the way to The Baths.
I would not suggest Moskito Cut if you have done it and know it, easy way to end your charter right then and now.
Many charter Companies do redline that passage.