If your flight arrives on time, I would think you could be at the ship between 1:30 and 2:30. Since you have transfers, you don't have to worry about claiming your luggage. Just meet the cruise reps in the main terminal, they'll take you to the bus area. It is a 45 min drive to the port. You'll have you forms filled out and in the little envelope they give you, so checking in should take about 5 mins, since there won't be any line. Then onto the ship. You may make it for lunch, but it may be close. One of the locations, Topsiders or Parrot Cay close a little later.
As for Palo, be flexible with you night and time, and you'll probably have no problem. But if in the unlikely event there are no slots left, don't give up. Check with Palo every day, and maybe several times during the day for cancellations. I know they have a wait list, but don't rely on just that. There are always cancellations.