Two key things that the OP should get out of this thread:
(1) When you are a diver coming off of a cruise ship, it is NOT that the Dive Op is treating you as a second-class citizen, but you ARE an unknown to that Op, and EVERY Dive Op on Cozumel that I know of is concerned for safety of their divers. There are several dive sites on Cozumel, like Punta Sur, Maracaibo, Santa Rosa Wall, Baracuda, that can be dangerous for an inexperienced or unskilled diver - no reputable Dive Op will take an unknown diver to any of those sites until the DMs have seen you and how you handled yourself on the easier sites. So a diver just doing one day of diving from a cruise ship is just not going to see those sites unless he charters his own boat and takes a private DM with him.
(2) The conditions at various sites on Cozumel can vary from day to day, or even during the day. Tormentos can be a calm easy drift dive one day, and a rip roaring bronco ride the next. Most Dive Ops won't plan which dive sites they are going to visit far in advance. The Captains and DMs, with long experience on the Island, will consider the conditions, the winds, the currents, and figure out which dive sites are best on a given day.
Let me add my own advice. Do NOT use the Dive Op that contracts with the Cruise ship operator. You will pay at least 40-50% more (the Cruise Line takes a big kickback for organizing the divers), and likely get a cattle boat scheduled dive. If your ship is coming in at the International Cruise Ship Pier (the one way south, down past La Cieba/El Cid), the Dive with Martin shop is right at the end of the Pier, and while Dive with Martin is a budget operator, among the lowest priced on Cozumel, it is a very good operation and will get you some good dives. It even offers free rental gear, if you haven't packed all your dive gear onto the cruise ship. I have dived several times with Dive with Martin, and it has a solid following here on SB. If you are coming in at the Punta Longosta Pier, at the south edge of downtown, there are several excellent downtown Dive Ops, and one ought to be able to make arrangements to take a diver off the cruise ship - try Aldora, Blue XTSea, Liquid Blue, Tres Pelicanos, Dive with Allison. Don't be surprised if some say no, because its boats are full or scheduled to leave before your cruise ship comes in; just keep trying. And if all else fails, go back to Dive with Martin, even if it means a couple of long taxi rides. STILL cheaper than the kickback the Cruise Ship is taking on its own charter Dive Op.