S. Taylor Harris was a British musician who was commissioned by the music publisher Boosey & Hawkes to arrange a few sea songs for publication. I believe the title was "Five Sea Shanties." The score appeared in 1925. This publication appears to have beeen Ives's ultimate source.

In the mid 50s, Taylor Harris wrote in the magazine "Sing Out!" that he'd collected "Hullabaloo Belay" from a sailing-ship man who could remember only the first stanza and the chorus. Facing a deadline, Taylor Harris decided to add some additional stanzas of his own invention. Thus the song as it is known today.

I am unaware that anybody has ever collected a second version of the song from a traditional source.