The version I learned in the late '50s-early '60s (on the playgrounds of West Allis, WI) was NOT to the tune "The Merry-Go-Round Broke Down" and was a truncated/loop version of some of the lyrics above:

"Helen had a steamboat, it had a little bell.
Helen went to heaven, the steamboat went to
Helen had a steamboat, etc."

Linn