I sailed on the Carnival Freedom from Port Everglades on 11 Jan. We drove to the port, got there around 12:30. We were on board and eating lunch by 1:45. Not too bad. I don't recall how many other ships were there, I remember seeing a Celebrity ship and a Holland America ship.
We were a bit on the later side, so we didn't have to deal with the people disembarking. That would make for a madhouse in the parking area.