I'm resuurecting this thread because I've just found more information about the term 'eastman'. In a 1911 paper in Journal of American Fok-Lore, 'Negro Folk-Song and Folk-Poetry' Howard Odum writes about a song entitled 'Eastman':

"The negroes have appropriate names for many of their typical characters, the meaning of which is difficult to eplain. "Eastman," "rounder," "creeper," and other characters, have their own peculiar characteristics. THe "rounder" is more than the idle character. He becomes the meddler in the home. The "Eastman" is kept fat by the women among whom he is universally a favorite. The "creeper" watches his chance to get admittance into a home, unknown to the husband. The "Natu'al-bohn Eastman" gives a view of his opinion of himself, with adopted forms of burlesque.

I went down to New Orleans
To buy my wife a sewin'-machine,
The needle broke and she couldn't sew,
I'm a natu'al-ohn Eastman, for she tole me so.

I'm a Eastman, how do you know?
I'm a natu'al-bohn Eastman, for she tole me so.

Well, they call me a Eastman if I walk around,
They call me a Eastman if I leave the town,
I got it writ on the tail o' my shirt,
I'm a natu'al-bohn Eastman, don't have to work.

Oh, I'm a Eastman on the road again,
For I'm an Eastman on the road again.

Wake-up, ole rounder, it's time to go,
I think I heard dat whistle blow,
You step out, let work-ox step in,
You're a natu'al-bohn Eastman, you k'n come agin.

Carry me down to the station-house do',
Find nuther Eastman an' let me know.

Wake-up, ole rounder, you sleep too late,
Money-makin' man done pass yo' gate,
You step out, let money-makin' man step in,
You a natu'al-bohn Eastman, you can come agin."