Looks like there was a radio show prior to the KPFK one in 1962. In the July 1961 letter below, Bukowski says that the first poem is "Hooray Say the Roses." The first poem in the 1962 show was "Prayer For Broken-Handed Lovers."
Time must be taking a toll on me, I had completely forgotten about that old thread talking about the same 1961 radio show. Well, the July 1961 letter confirms that the radio show actually took place and B seems to be proud of it.