Carter, here's one more incarnation, collected in the Ozarks in 1951. And there's audio!:


https://digitalcollections.uark.edu/digital/collection/OzarkFolkSong/id/4568/

Unlike "I Can Whip the Scoundrel, the tune is closely related to "The Derby Ram" and "Blow Away the Morning Dew." I'd call it a different song.   

A very similar text, from the Raleigh Times (Apr. 14, 1898), p. 2:

                         AN OLD WAR SONG

A lady yesterday sent to The Times the war song published below and which, she says, has not been printed for thirty years. The copy from which this made is old and worn.

                         ON TO RICHMOND

On to Richmond, early in the morning,
On to Richmond, I heard the Yankees say.

We have the navy, we have the men,
We are bound to Richmond, to storm the Rebel den.
On to Richmond, &c.

We'll flank her on the north and shell her on the south,
Storm her in the centre, run the Rebels out.
On to Richmond, &c.

But Lee was in the centre, Jackson in the rear,
On the right and left did the noble Hills appear.
On to Richmond, &c.

Longstreet they had to travel, Bramch they had to cross,
Magruder was about to give the Yankees goss.
On to Richmond, &c.

About the first of June the balls began to fly,
The Yankees wheeled about and changed their battle cry.
So off from Richmond, early in the morning,
Down to the gunboats, run boys, run.

Virginia is coming with her death-dealing steel,
Georgia is charging through swamp and field.
Off from Richmond, early in the morning,
Down to the gunboats, run boys, run.

The Palmetto Rebels are now on the trail,
North Carolina devils to ride us on a rail.
Off from Richmond, &c.

There's the Alabama Rebels, bound to win or die,
The Mississippi rifles, fly boys, fly.
Off from Richmond, &c.

Louisiana legions, Butler is their cry,
Texas bloody rangers, fly boys, fly.
Off from Richmond, &c.

Florida is hunting all through the bush,
The Rebels are in earnest, push boys, push.
Off from Richmond, &c.

Never mind your knapsacks, never mind your gun,
This fighting with the rebels is anything but fun.
Off from Richmond, &c.

A farm was the promise, and each man a slave,
We had better all skedaddle or we'll find a grave.
Off from Richmond, &c.

McClellan is a humbug, Lincoln is a fool,
Seward is a liar of the Horace Greeley school.
Off from Richmond early in the morning,
Down to the gunboats, run boys, run.
   Petersburg, Aug. 1862.


To "give goss" means to "give hell" (well, "heck" actually.)