If you're getting there a day early, I've done some investigating on the transportation to Port of Miami from either airport. Avis car rental is the only company that has a drop off site at the Port. I've checked and you have to make your reservation by phone and tell them you want to pick-up at the airport (Ft. Laud or MIA) and drop off at the Port of Miami (MIO) and they will set it up. You can reserve all types of vehicles, if you have a coupon for an upgrade you can use it. I upgraded from a compact to an itermediate for less than $40.00. We are traveling 4 people and this seems to be fairly reasonable.
I agree, I am cruising in June and we are getting a car for the day when we get back, Avis seems to be the best bet due to the fact they shuttle you to the terminal. Seems any other way you would have to get to the rental site by taxi.