Well, some of it depends on whether you are going to base yourselves on the mainland or on Cozumel (and whether the purpose of your trip is the class, or the class is incidental to open water diving). If you are going to dive off Cozumel, you can do the cavern class there on the island with German Yanez. He was Peter's and my cavern instructor, although we did not do our class on Coz, and he was also the cavern instructor for HBDiveGirl, who DID do hers on the island. German is a lovely, happy, patient man who has done a lot of the exploration of the caves on Cozumel, and knows a lot about the unique life forms that are found there.
If you are going to base yourselves on the mainland and focus on cavern diving, I would highly recommend Dennis Weeks of Aquanauts (he is Pez de Diablo on this board). Dennis is also an extremely nice man, and my husband has done guided cave dives with him, and likes him a lot and was very pleased with his attention to safety.
I don't know when you are going to do Fundies, but if you have done that before you go, you can do guided cavern dives with the Zero G guys. I did my very first cavern dives with Danny, and you cannot imagine a more thorough and organized guide. Zero G does not teach a cavern class, however; GUE does not think a cavern class is sufficient training to operate independently within the overhead environment. I tend to agree with them, but I did my cavern class as a stepping stone to further cave training, and it served that purpose very well.