The only time I did DT I wasn't even aware we were there until we came on the entrance. I had been at the entrance before and recognized it, so we checked our air (nitrox) and dropped through. AL80, not at the start of the dive.It is hard to understand how not going past NDLs on nitrox when you went way past them on air means nitrox provides no payoff.
BTW, Cathedral and Devil's Throat are not the only Punta Sur Dive sites, but no one dives the third (can't remember the name) much. About 10 years ago or so, diving with Aldora with Memo as the dive guide and using 120s with nitrox, we did all three on one dive. Memo called it "active nitrox diving."