The long lost footage of McLean Stevenson as Col. Henry Blake has finally surfaced, thanks to the fine folks over at www.mash4077tv.com. Maybe part of the reason this clip--which supposedly aired just days after "Abyssinia, Henry"--was so hard to find was that it was always credited to The Carol Burnett Show (it even says so on IMDB).
But as you can see from the video above, this weird cameo was on a Cher-hosted show, mostly likely the 1975-1976 variety series simply known as Cher. IMDB lists Season 1, Episode 7 as having aired on March 23, 1975, just five days after the legendary M*A*S*H Season 3 closer. There's no mention of the appearance of course, but I feel like this is a safe bet.
A tip of the martini glass to Swamp Rat Daniel Hopmans for letting me know about this. As Hawkeye Pierce once said, I hate a mystery!