That Mikado was special for me, as seeing both that and the old Kenny Baker film on TV within a relatively short time were my introduction to Gilbert and Sullivan. I believe the Groucho was only shown once, live, and I was thrilled to find it on DVD several years ago.
The Amahl that I know we saw, which I loved, was the 1964 telecast which, to my knowledge, remains unavailable on any home video format. That recording of it remains one of my favorite things.