Agreed about the long wait at the airport. Here's my suggestion...
Check the bags as if you're going to stay at the airport. I'm assuming the cruise ship is going to drop you there anyway.
Take a cab to FTL beach and have brunch/lunch around 11:00a or so. The beach is maybe 20m max even with traffic (using 17th St. causeway).
Be back at the airport by 2p to get through security. It's usually a mess on cruise ship days and they start calling folks into the line based on flight departure time.
Have fun!