I have to disagree with you on the 2:00 PM boarding. On all of my cruises the latest I have ever boarded is 1:00 PM. (Legend in Fort Lauderdale) If you show up at 9AM or 10AM you will have a LONG wait and just setting yourself up for frustration. The staff does have to disembark the returning passengers, turn the ship, take on provisions and put on new smiling faces for the next 2,000 + arriving cruisers. I'm always amazed at how they can do this in about five hours. On a few occasions my cabin hasn't been ready but I've always been able to drop my carry-on and head upstairs for lunch.
I have found the best time to show up is around 11:30 AM. A 2:00 PM boarding will put you in the most congested time with the cruise air passengers. (U.S. Caribbean cruises). Granted if there is a customs/immigration problem, such as drugs or people smuggling you are going to wait a long time.