Now I have a catchy tune! Awesome parody, Donna - I chuckled heartily at that.
But man is that second blank difficult to fill! Nothing rhymes on "women" that would make sense with Butler's departure from New Orleans. I found several sources (among them
Scarred by War: Civil War in Southeast Louisiana (p. 199) and
Butler's memoirs (p. 532-533)) that say Butler handed command over to Banks on December 16 but left the city only on Christmas Eve, December 24.
This site says he left on December 16, at 10 o'clock. Ignoring the obviously mistaken date of change of command with physically leaving the city and since I can't find anything else that would fit the "right at" in front of the blank, I'm going with 10 o'clock though it doesn't rhyme with "women" and no other source had any indication as to a time of departure.
The folks of New Orleans gladly said adieu
in the year of the Lord - Eighteen
Sixty-Two.
there were smiles on the faces of the many women
when he left that morning right at
10 o’clock.
Butler the Beast - from the northeast.
Our hate is deep, your leaving is sweet,
We’d like to forget - but we’ll always remember,
when we said goodbye on the
24th of
December.
I'm probably going to slap myself senseless for having been stupid once the answer is revealed but right now, after having trawled the internet for a good three hours, I'm at a loss what else it could be.