So, if I were looking at two dives a day at 77 degrees, I'd probably dive a 3mm and a hood, but Socorro is usually a dive-a-thon and you're in your suit for long time, relatively speaking, by the time you gear up (in a wet cold suit), get on the rib, to the drop, back on the rib, pick up divers, and get back on board. Your core temperature will drop by over the course of the day.
There are also occasional upwellings of colder water. People are different, but my advice would be whatever your "normal" comfort requirements are, you should err on the side of some additional insulation.
In 81 degree water at the beginning of December everyone was in 3mm, at least, except for a just a couple of people that wore Lavacore-type tops (and did not look comfortable by the end of the day.
Last and related to tbone's comment about DCS risk, there were folks that were warming up at the end of the day in hot showers and even a hot tub (yes, the boat had one). That's a great recipe for getting skin bends, which is what happened to one of our divers. The moral of the story is stay warm on the dive, whatever it takes for you to do that.