Paul,

Papa Charlie Jackson's 1925 version (recorded in Chicago) is basically the same as you've posted with just a few variations. He doesn't sing the first verse you post at all, he starts with your second verse. Your third verse is his second , but he sings 'Charleston' not 'chocolate'.

The next verse is the same, and in the following verse Jackson sings 'Now get back, show me, they're dyin' to do./ Let your mammy show you just how to do.'Then the next verse is the same.

Following this (the bit you're interested in) Jackson sings the following verses:

Now Grandpa Johnson grabbed Sister Kate,
She shoke it just like she shakes the jelly upon the plate.
We're gonna shake that thing.
Aw, shake that thing.
I'm gettin' sick and tired of tellin' you to shake that thing.

Now old Uncle Jack, the jelly roll king.
He just got back from shakin' that thing.
Now he shakes that thing.
Wants a little more to shake that thing.
I'm gettin'sick and tired of tellin' you to shake that thing.

Now old Uncle Moe, he's sick in bed.
The doctor says he's almost dead.
From wantin' to shake that thing.
Wants a little more to shake that thing.
I'm gettin' sick and tired of tellin' you to shake that thing.

Now the folks in Georgia they've done gone wild.
The hold of this dance is settin' the style.
They call it Shake That Thing.
Aw, Shake That Thing.
I'm gettin' sick and tired of tellin' you to shake that thing.

Kokomo Arnold also recorded a version of this song (in Chicago in 1936). He recorded fives verses, four the same as Papa Charlie Jackson and this one:

Says now I see it's just a little funny swing.
You don't need no lessons to shake that thing.
Keep on shakin' that thing, keep on shakin' that thing.
`Cause I'm so sick and tired of tellin' you to shake that thing.

Also, in 1932, the Mississippi Sheiks recorded 'New Shake That Thing'

So cold up North till the birds can't sing.
The people down South, shakin' that thing.
Oh, shake that thing, oh, shake that thing.
Well, the people down South will always shake that thing.

I laid down last night, I was awful sick.
I woke up this mornin', she had my toecaps fixed.
So I could shake that thing, so I could shake that thing.
I went down to the station, up to the train.
I couldn't buy no ticket for shakin' that thing.
Oh, shake that thing, oh, shake that thing.
Well, the people down South will always shake that thing.

I went down to the railroad, I laid my head on the track.
The train come along and it broke my back.
Now, I can shake that thing, know I can shake that thing.
Well, the people down South will always shake that thing.

Hope this helps.

Brian