There was a champagne glass feature until H.Gilbert in 1988 or so the story goes. That was twenty years before my first visit to the island, I don't think I have been to that location. Maybe Gordon remembers? Cozumel Mexico Beaches El Mirador (The Looking Glass).
Gilbert was in 1988 and the spring of that year is when I started going at least once a year until COVID-19 scuttled my trip in 2020. I did go there two or three times between 1978 and 1988, and I have visited El Mirador on every trip, but I don't remember anything like he describes. El Graduado would be the one to ask about it.