Since posting it and listening to the song again (and again), I've been envisioning how Zero Mostel must have performed it every night, and it became heart-breaking to know that no recording of him doing it exists. I decided to see what I could to find out if that was the case, so I went to the source and asked the show's lyricst Sheldon Harnick. (I have to admit, it's nice when you can do something like that...)
He wrote back that as far he knows, there "was never a recording of Zero" doing it. However, he added a reminder of a related bit of information from an earlier exchange. "As I think I mentioned, he loved the song and his were the loudest protests when we cut it!"
I can only imagine. In fact, that's what prompted my asking if any recording existed. Whether or not the song worked in the show, I suspect that Zero Mostel's performance of it was remarkable. Listen to the song again, but this time not with Sheldon Harnick singing, but put in the voice of Zero Mostel...