LL Bean rolling duffles are a good way to get a lot of luggage out of the way. You can also ask your charter company if they have somewhere to store luggage once you unpack on the boat. We've left luggage in a couple different charter offices as we've gone off sailing.

I don't know if you can get to Anegada on a week of sailing out of Red Hook because I think you have an extra day on each end just to get to/from BVI. We've always left out of Tortola. If you have a professional crew, maybe they are more comfortable sailing later in the day and could do it. In general, our route looks like this -

Bight (dive the Rhone)
Cooper (explore the Baths)
North Sound (dive the Dogs)
2 nights Anegada (first order dinner at Wonky Dog, then rent a Moke, snorkel Loblolly, then drink at Cow Wreck, dinner at Wonky Dog - bring bug spray.)
Great Harbor (Dive JVD, afternoon at Soggy Dollar)
Bight (Lobster dinner at Pirates is pricey, but good)

We are divers and would suggest diving on the Rhone (2 tanks - bow section and stern section,) the Dogs, and out near JVD. There are dive shops that can rendezvous with you at the Bight or Cooper for the Rhone, North Sound or Marina Cay/Trellis for the Dogs, and Great Harbor for JVD. If your divers are confident navigators, they can also load up gear and tanks onto your sailboat and lead their own dives (save a lot of time and money!)

If you're based in the USA, call your doctor and ask about Scopace. It's a prescription seasickness patch you wear behind your ear, so you're getting a constant low dose of medication. It has worked miracles for my husband and most doctors will prescribe it without a visit unless you have something that is contraindicated. Try it at home for a day so you aren't surprised by any side effects and also do not touch your eye without washing your hands after putting on the patch. (Edit: Husband reminded me that Scopace is the tablet form of the medication. Trans-Scop is the patch. The actual medication is called scopolomine.)