I decided to look for the copy of this performance that my friend made for me, which has been missing for awhile, and I found the box containing it and other videos I've been missing. So, I can tell you that the year was 1986, since they said it was 22 years after the Kirov's last North American tour, which they say was in 1964. (But that means I'd have been 13 or 14, and I know I was older than that when I last saw the Kirov live, and in the souvenir program for the season I saw, the listing of performers Sol Hurok was presenting was for the 1965-66 season.)
Lilac, do you still have the tape you made? In case you don't, here's a bit of trivia from Ronald Reagan's introduction: this performance was the first major performing arts presentation in the US under the exchanges agreement that was signed at the meeting of Reagan and Gorbachev at the Geneva Summit.
The artistic director at that time was Oleg Vinogradov, who is interviewed, and who says he's contacted Robbins, Joffrey and Graham about the possibility of presenting their works at the Kirov, "where our dancers are so versatile that they can dance whatever style is presented to them." (I don't know, somehow I don't think they'd have such an easy time making Graham look right.)
I couldn't stay up late enough to see the credits at the end, but I recognized the principals, Olga Chenchikova and Konstantin Zaklinski. I watched the first scene, and can tell you that one of the women in the pas de trois is Zhanna Ayupova, and I think the other's first name is Nina, but I'm not sure of her last name (Chistyakova??). I didn't recognize the man, who has curly blond hair. The production is Konstantin Sergeev's, and it seems to be the same one that's on the 1990 video with Yulia Makhalina and Igor Zelinski, except in that one, the prince is the man in the pas de trois.
Since my friend doesn't believe in distributing copies of videos that are commercially available, the very fact that he made this copy for me makes me pretty sure that it isn't available.