I see now that Lighter has posted a couple links to the Flight of the Doodles previously.   The text I'm pasting below is almost identical to the version from his 02 Feb 14 - 07:46 PM posting, which cites "Poetry, Lyrical, Narrative, and Satirical, of the Civil War," but this one does come with an (albeit, nearly unquantifiable) introduction to the source. It also carries the variation for diff-a-bitterance in Louisiana.

The earliest version of Flight of the Doodles, from 1862, printed in Rebellion Record by Frank Moore, Poetry and Incidents, p. 51

The following was found in the camp of the First Texas Regiment, by a member of Co. G, First Massachusetts Regiment.

I come from old Manassa [sic], with a pocket full of fun —
I killed forty Yankees with a single-barreled gun;
It don't make a niff-a-stifference to neither you or I,
Big Yankee, Little Yankee, all run or die.

I saw all the Yankees at Bull Run,
They fought like the devil when the battle first begun.
But it don't make a niff-a-stifference to neither you or I,
They took to their heels, boys, and you ought to see 'em fly.

I saw old Fuss and Feathers Scott, twenty miles away,
His horses stuck up their ears, and you ought to hear 'em neigh,
But it don't make a niff-a-stifference to neither you nor I,
Old Scott fled like the devil, boys, root, hog, or die.

I then saw a "Tiger," from the old Crescent City,
He cut down the Yankees without any pity—
Oh! it don't make a diff-a-bitterence to neither you nor I,
We whipped the Yankee boys and made the boobies cry.

I saw South-Carolina, the first in the cause,
Shake the dirty Yankees till she broke all their jaws—
Oh ! it don't make a niff-a-stifference to neither you nor I,
South-Carolina [sic] give 'em h —ll, boys, root, hog, or die.

I saw old Virginia, standing firm and true,
She fought mighty hard to whip the dirty crew—
Oh! it don't make a niff-a-stifference to neither you nor I,
Old Virginia's blood and thunder, boys, root hog, or die.

I saw old Georgia, the next in the van,
She cut down the Yankees almost to a man—
Oh! it don't make a niff-a-stifference to neither you nor I,
Georgia's sum in a fight, boys, root, hog, or die.

I saw Alabama in the midst of the storm,
She stood like a giant in the contest so warm—
Oh! it don't make a niff-a-stifference to neither you nor I,
Alabama fought the Yankees, boys, till the last one did fly.

I saw Texas go in with a smile,
But I tell you what it is, she made the Yankees bile—
Oh! it don't make a niff-a-stifference to neither you nor I,
Texas is the devil, boys, root, hog, or die.

I saw North-Carolina [sic] in the deepest of the battle,
She knocked down the Yankees and made their bones rattle—
Oh! it don't make a niff-a-stifference to neither you nor I,
North-Carolina's [sic] got the grit, boys, root, hog, or die.

Old Florida came in with a terrible shout,
She frightened all the Yankees till their eyes stuck out—
Oh! it don't make a niff-a-stifference to neither you nor I,
Florida's death on Yankees, root, hog, or die.

* * * * * * * * * * * * * * * *

Beyond this book and the one Lighter shared, the only other two sources I've found were a widely-published syndicated column from 1883. Here's the text from the earliest edition I found online, printed in the May 21, 1883 edition of The National Republican (Washington, DC), p. 3:

" The Battle of Manassas, or Bull Run, as it was known at the north, called out many stirring poems, calculated to renew the courage of the southern people, and fire them to renewed exertion for independence. Among the most graphic of these, and with a certain humor in it was one entitled, "Flight of the Doodles." A few sample verses must suffice: "

It goes on to repeat stanzas 1 and 3 of the above nearly verbatim.    In 1909, Benjamin Harvey, a Tacoma businessman and writer for The Tacoma Daily News exercised a case study in plagiarism by re-writing that article almost in its entirety. Published in the February 12th, 1909 edition of the paper, it adds nothing new here; I mention it solely for the fact that it's the most recent reference Ford and his companions could have found the poem in I've been able to identify online.