We used to love cruising until we discovered diving in Cozumel. DWM was our first op when we took a cruise to Coz for our first blue water dives. It will take longer to get off the boat than it will to walk to the dive shop. Shoot them an email and see what they can do. We had 4 divers in our group so we were able to charter our own boat and it was waiting on us when we got there. Im sure there are cruiser forums, maybe even on Scubaboard, that you could meet up with other divers on your cruise to charter your own boat. I think Carnival had a boat specific forum to meet up with other people, other cruise lines may do the same.
I would not book with the cruise lines dive op unless you can verify they use 6 pack boats. At least find out which op they use and see what trip advisor reviews tell you. There is one that Carnival used to use, maybe still does, that will put 20+divers on a slow boat then give them crappy gear and short dives...no thanks.
As far as what reef, that is usually decided based on conditions of the day and the dive skills of everyone on the boat. It also matter on what you like. Deep swim throughs like Columbia deep or pinnacles are fun, but will shorten your dive. Shallow drift dives with lots of sea life are my old favorite, Franchesca, palancar gardens, Cedral, tormentos, are all great usually loaded with life like sharks, eels, turtles, and my favorite, trunk fish and cow fish. (They just look like Darwinian mistakes) If you're a wall guy Santa Rosa or I think there is another wall, but it's more like a steep hill.
My new favorite it Barracuda in a moderate current. Big Big fun. Almost hard to keep water out of your mouth from smiling so wide! Probably not an option unless you took a cab to a pick up point (villa Aldora?) in the far north. San Juan has gardens of finger coral that are beautiful. A north 2 tank dive could do San Juan And Barracuda, but you would probably have to dive with Aldora (they have a hotel with their own pier far north) to make that happen, otherwise your in for a loooong boat ride and may not have time.
Best case scenario, find 3 other divers to buddy with and charter your own boat with DWM. If that is not a workable deal, I believe Blue XTSea has a cruise ship deal as well, maybe Tres Pelicanos too, shoot them an email and see what they can do.
Good luck, safe travels. If you're on Carnival...have a chocolate molten lava cake...or 10... for me!
Jay