Is the boat provisioned?
You can easily leave Red Hook and get to an overnight anchorage close by if your boat is ready to go when you arrive - even a night around the corner at Christmas Cove is fine.
Visiting Anegada in the remaining 5 nights is possible but will be a lot of time underway and maybe a bit too much sailing for a new charter group.
Consider the cost of your group for the ferry and Tortola taxi VS. the cost of the pickup to compare - and C&I time and fees.