The Radisson shuttle does get booked early, and you cannot reserve a time until you check in. We arrived 6:00 pm Friday night, and the earliest shuttle available was 2:00 pm (much too late in our opinion). In the morning, I drove family and luggage to the port. Family had luggage checked, went through security, and got in line. I drove back to Radisson, parked in designated area, and went to Avis. I waited for about 15 minutes (I just missed a van) and then was given a ride. I was the only one on the shuttle, and I tipped a couple of dollars. The driver had to go back to the port anyway to pick up others from Carnival.
I was thinking we probably should have had the entire family waiting for Avis. But later, I ran into a fellow Dis who was on the shuttle that I just missed; he indicated it was full. Ultimately, I liked our decision to have family in Air Conditioned port, beyond security and in line for check in, while I did some driving.
We were set at the end of the trip to do the reverse (I go by myself in Radisson or Avis shuttle to pick up car, then come back for family and luggage). But the Radisson shuttle was waiting at the port and available. We all got on and were back to the Radisson by 8:45.
And I will second the comment about setting up a Dis meet at the Radisson by the pool. It was nice not having to figure out the time on Saturday to meet (after you board and make reservations, but before the safety drill, etc.) We also ran into everyone again at the Port and stood in the boarding line together.