I just got back. I rented a car from Avis and dropped it at the office close to the port. They took us right to the cruise terminal in their shuttle.
I had a car reserved for the day we got back. We left the ship, walked out of the terminal to the shuttle waiting area and the Avis shuttle took us back to the rental place for another car. I rented a full size car with the discount code from Costco and it was $50 total with tax and gas. (They have a $10.50 fill up deal if you drive less than 75 miles. We drove to Kennedy Space Center, spent the day, and then on to the airport for a total of 72 miles) So there's no worry with stopping at a gas station.
The trip from the airport to the rental car office is 46 miles. You pass the cruise terminal on the way to Avis, it's *maybe* five minutes away from the port.