The lyrics above shared by Comic Book Fan are what I was looking for and brought me here. Those lyrics were in the version played on Dr. Demento back in 1973, 1974.

Interesting background on the song from 1930 tells me the version I searched for is a parody of that original. In the '70s version, as indicated, it was clearly Pink Burrito, not Big Burrito. Dunno for no ice cream though.

Thanks, folks.