If you are going to take the boat you might as well stay a few days. It's a lovely spot and, as Dan says, by anchoring you can enjoy the islands before and after the tourist ferry leaves. There are, however, two problems in winter--the days are shorter giving less time to enjoy the solitude, and the weather is highly variable. You have to be prepared to stay there if the winds come up. The park has no facilities for food or fuel, and no cell phone service.
Fanfare was in Key West this spring. My kids and grandkids all took the ferry in March and April. They reported that this was fine. The ferry provides snorkeling equipment, breakfast and lunch. You MUST make advance reservations as they are sold out during spring break well ahead of time. Even on this large fast ferry the passage can be rough. I believe they have fairly liberal cancellation policies if you decide the weather is unsuitable although getting another time slot may be harder.
We kept the boat at the Stock Island Marina Village in Key West which may be the best marina I have ever stayed at. Certainly the cleanest! Staff was always helpful. Three of the best restaurants are nearby. It is away from downtown bustle but the hotel has an free hourly shuttle to take you there or to the supermarket or the beach (20 minute ride). I have already reserved a slip for next year. See you there!