I think it is doable since you are on a power boat. We only had 6 nights in November and were able to get it all in without feeling rushed. My kids actually thought it was the best one yet! We decided that rest time was for passages, except for the person on watch of course. You have a captain so that's his job!

4/4: Cooper (get on Boaty Ball in the morning see if you can reserve a ball)
4/5: Leverick (get up early and have a car reserved and ready for you in Leverick when you get there)
4/6: Anegada (as I said previously, I recommend renting a car so you can see more of the island.
4/7: Jost
4/8: Norman or Cane Garden Bay (agree with George of a stop at Indians, we also checked out the caves in November, which we hadn't done in years and it was pretty cool)
4/9: Return boat

We have also done Anegada to Diamond Cay and then White Bay/Great Harbor the next day and returned the boat from Jost rather than Norman the last night. Diamond Cay is fun with B-Line, Foxy's Taboo (like this way more than Foxy's now) and Sandy Spit.