I used to live in Orlando and the port is about 50 miles away. I could only imagine how much the cab fare would be. You might want to consider the $30 fee from Carnival.
When I traveled on the Disney Magic a few years back, I drove over and parked at the port. Was pretty convenient at the time for me. You might even consider renting a large passenger van that you might be able to get with a one way drop.
I haven't done it yet but I am researching the same thing for my Pride cruise in April.
With a party as large as yours, you should check out the transportation companies that have vans. Two that I have heard good things about is Tiffany Towncar and yourride.net. You should be able to get roundtrip transportation for less than the Carnival transfers. Plus, you can determine the times since it would just be for your party. I haven't made a decision yet, but I'm planning to do this and we only have 3 in our party. I just think it will be more convenient.
I've been researching this myself. I would up booking with Basik Shuttle (1-877-459-1177) for $65 each way for two people in a van. They were the cheapest. I believe for $10 more you can take a Towncar. Good luck!