I'm wondering if you're not mistaken about the Chicago radio broadcast? The Dead came back to Chicago to play on 10/21 and 10/22; the 10/21 show was broadcast on 10/22.
I have a hard time believing there was also an August Chicago FM broadcast that was completely lost by radio-tapers at home. The FM broadcasts on the fall tour were, I believe, paid for by Warners to promote the new live album.
