More on that That's Singing special. My pal Geoffrey Mark writes that it had a strange history…
Ethel Merman's and Mary Martin's parts, along with about two-thirds of the show, were taped in 1980. Some of the other numbers were taped separately a couple of years later for a PBS thing that never aired. They were cobbled together and shown in 1983, after Merman had her stroke but before she died in 1984. It was then repeated on PBS a couple of times after she died.
And then Michael Frank writes to say that IMDB says it aired on PBS on May 24, 1985. Thanks to both of you.
Since we're talking about Merman on that special, here she is, boys…