Another option would be to head over there the day before and book a room at a nearby hotel - a number of them do a stay + park deal much like the airport hotels do over here.
A few years back we stayed at the Radisson, as there are a couple of restaurants in walking distance and they have a shuttle to take you to port which seemed pretty well organised.
It's also handy if you have plans to visit Kennedy Space Center which is just a few miles away