The anecdote about Gilmore in New Orleans comes from Irwin Silber's usually reliable Songs of the Civil War (1960). However, in a 1988 article in the journal "American Music," Frank C. Cipolla quotes Gilmore's words directly (from "The Musical Herald" of 1883):

"[The melody] was a musical waif which I happened to hear somebody humming in the early days of the rebellion, and taking a fancy to it, wrote it down, dressed it up, gave it a name, and rhymed it into usefulness for a special purpose suited to the times."

No mention of an African-American (or Irish) source here. Also, as Cipolla points out, Gilmore did not arrive in N.O. until January of 1864, long after "WJCMH" had appeared.

When Francis O'Neill printed the famous tune in "Waifs and Strays of Gaelic Melody" (1922), he preferred to call it "Johnny I Hardly Knew Ye" instead of "Johnny Fill Up the Bowl," as in 1903 (though O'Neill's 1903 index did list "JIHKY" as an alternative title). He confidently asserts that the "spirited air was almost forgotten in Ireland" until the Irish-born Gilmore's "master hand" revised it during the Civil War. Oddly, only the 1922 version has enough bars to fit the four-line chorus of Geoghegan's lyrics!