I feel a little dumb not to have mentioned "Johnny I Hardly Knew Ye," the obvious precursor to which "When Johnny Comes Marching Home" was the published answer. "Hurroo, hurroo" may even be a trace of the original refrain, and thus of an earlier song.

My bet: there is a tune/song preceding "Johnny I Hardly Knew Ye."

By the way, Willard Heaps in The Singing Sixties (a history of Civil War song) mentions, together with "For Bales," two other Civil War parodies: "We Are the Boys of Potomac's Ranks," to the "stone blind" chorus, and "When Abe Comes Marching Home Again," with a chorus "And we'll all be free when Abe comes marching home."

Bob