Renting a car would be the easiest way to go and a lot cheaper than that private transfer option. Get a taxi from Port Everglades to the Fort Lauderdale airport (about $20), rent a car there, then drop the rental car off at the Miami airport on your way out. All of that together will cost a lot less than $220. We're doing that for our upcoming trip, and the one-way Enterprise car rental from airport to airport is less than $100.
I will caution you against renting a car from near the cruise port. The post-cruise shuttle situation from the cruise port to the nearby car rental place can be awful, and prices are usually higher than from the airport. The FLL airport is not far from Port Everglades. Just get a taxi (they're waiting when you get off the ship) and take it to the FLL airport, and rent your car there.