Take a look at the tune given in Goodenough's book (link in Jim Dixon's post of April 9, 2011). The melody is solidly in the key of F major, yet the final note printed is an E. Has to be a typo, don't you think? If not, that puts quite a twist to it. Perhaps, in keeping with the seemingly absurd lyrics, ending with such a dissonance was all part of the fun.

Jerry