I guess it's no secret that I'm a big fan of Princess. I've done the Ft. Lauderdale to Los Angeles cruise twice: first as an 18 day that was actually a back-to-back (Panama Canal and Mexican Riviera on Sea Princess); and more recently the Exotic Panama Canal on Island Princess. It was 15 days when I went but they have cut Ocho Rios and it is now 14 days.
I"ve done the cruise in April and in May; weather was perfect both trips. I hear it is unbearably hot in the Summer; and of course hurricane season in the fall.
Sea Princess, Royal Princess and Pacific Princess only have one sailing each. Island Princess and Coral Princess have several different itineraries. I like the Exotic itinerary because you get a chance to see Nicaragua and Guatemala. Huatulco, Mexico is nice too, but like Ixtapa, a master-planned resort destination--which is okay, but kind of sanitized.
You can also see Guatemala, Nicaragua and Huatulco on the 10 day Panama Canal Adventurer and the 18 day and 20 day Grand Panama Canal. There is also a 19 day Pacific Panama Canal, but it dosen't make a full transit of the canal. I think the Exotic at 14 days may be just right for you.
Hope this helps a little. I also just posted some shore excursion suggestion for this itinerary in the Princess Cruises forum for another member. Anything else I can help you with, please just ask.