We are flying in a day early because I am too afraid to miss the boat.

I have found the hotels at the Cape offer round trip transportation to the airports and the boats with reasonable rates. You can purchase private and shared shuttles depending on your priorities. I have seen talk about cruisers being frustrated with slow shuttles to the cruise terminal though.
Here are the Radisson rates:
Orlando International Airport (MCO) Transportation Pricing:
1 Person: $33.00 USD Flat Fee, One Way
2 Persons $50.00 USD Flat Fee, One Way
Each additional person: $10.00 USD Flat Fee, One Way
Lincoln Town Car (max 2 people): $105.00 USD Flat Fee, One Way
Renting a car can be cheaper but you will have to deal with the and pickup/return .
This was one of my big issues early on in booking this cruise. Hope this helps.