G'day Mark (and Barry),
Somewhere, deep in my tape collection, I have a recording of the original of this story ... before it became a song. It was an address to the Oxford Society by the wonderful (and very musical) cartoonist Gerard Hoffnung. This was presented as a humorous monologue and the song just sets a tune to virtually the same words.
It may be heresy in this company, but I think the humour works eevn better as spoken word. I know that a lot of the humorous songs I sing do not gain from accompaniment, which often fights the free play of tone and speed that is essential for good comic delivery.
That said ... it is a bloody funny song!