We were trained to the NSS standards using the NSS Cavern Diving Manual, which states that the limit is 130 linear feet and 70 feet in depth.
Morrison is a great cavern dive and as for safety I would put it up there with the cavern at Ginnie. You cannot get out of the day light zone unless the area is flooded. Ginnie lets open water diver go in their cavern. Now I am not saying Open water divers should be going in Morrison but there are exceptions to the rule. The biggest issue I see with Morrison is the chance of a panic diver. Morrison seems a little more restricted entering the cavern and it is a little smaller but I guess you could get a panic diver at Ginnie. All in all diving the cavern at Ginnie or Morrison If you dont understand what you are doing then get educated and get the Proper training, if you start to feel uncomfortable, turn the dive.