We took a car service from WDW to the port for our late September cruise on the Dream (we traveled in a group of 7, 3 cabins total). Everything went very smoothly. We had a 12:15pm PAT, so our car picked us up at 11:00 am and we arrived at or just after 12:15pm. I've only heard of issues if you arrive too early for your PAT; they will have you leave the area and wait until your PAT to enter.
Cast members met us at the curb to take our checked luggage and then we were guided over to the testing tents, swabbed (stay with whoever is in your cabin), then told to wait in the air conditioned waiting tents until our results were ready to view in Safe Passage (took about 35-40 minutes). We were then escorted over to the terminal to check our travel documents (we had to go to the help desk in the terminal to verify some documents since some members of our group have foreign passports), go through security, and then board the ship. All in all, I'd say it took about 1.5 hours from the time we dropped off our luggage until we were up in Cabanas.
Keep in mind that we were asked to show our QR code from the Port Arrival Form multiple times throughout the boarding process, so keep the printouts or your phone ready to whip out.