In 42 Disney cruises, we've done the transportation just about every way possible. I, too, am a big advocate of arriving the night before. Our most common method is getting an airport hotel via Priceline ($25 to $33 for a top star level) and having Happy Limo pick us up the next morning. If you use the Disney buses, you can take the hotel shuttle back to the airport. But personally, I don't like "cattle calls," so I prefer a towncar.
I've also rented a car each way from Budget, and that's pretty painless. You will have to wait for a shuttle both ways, and I've seen some horror stories, but I've never experienced one personally. On our cruise last weekend, we parked at the port...got there before 11 a.m., and there was no crowd. Hubby dropped me off at the terminal building and then parked the car.
Barb