Regarding the radio show, I'm going from memory of something I read a few years ago. By all means, correct me if I'm wrong.
It's possible that he never wrote for the radio, but he was credited with creating the character of Sam Spade. Maybe what I remember is that the credit was removed as a result of his activism - rather than him being fired as the writer.
I also remember reading that he was very sick in the last few years of his life (he was a heavy smoker and drinker), to the extent that he didn't have the strength to write a single word of anything.
Currently reading: Why Was Queen Victoria Such a Prude? (David Haviland); Payment Deferred (C.S. Forester)