I'm on a pretty similar mission that week. We have friends that want us to show them around and I am reluctant. The 4th of July week is always the busiest of the summer. The Harbormaster at Block Island told me they had 2500 boats in Great Salt Pond last year for the 4th. From having started some calls for reservations on the Vineyard and Nantucket, those are mostly full too. Not at all surprising.
To amend a point made above, the outer harbor of Vineyard Haven does have a lot of room, but the fetch is horrible in North or Northeasterly winds. As in, get no sleep at all. Be warned.
Good luck and try to have fun. Flexibility and patience are going to be key to make that week work. Given the 4th is on a Wed, I suspect Mon and Tue will be okay, then it will become an invasion through the weekend.
You won't fit in Katama Bay assuming your boat is the Jenneau 54. Look at what I was talking about before, and you would be in prime location for the fireworks!