I expected to find that the expression "balling the jack" was older than the song, but I failed to find any examples. The closest I could get was this: from The Freeman, an Illustrated Colored Newspaper, December 20, 1913, page 12:

ANNUAL STAGE REVIEW
The Parliament of Intellect as a Lost Cause in a Valley of Imbecility
Immoral Sarcasm—Managers and Alliances—Colored Shows
The Southern Situation—Picture Houses—Artists Illustrated
. . .
Cost of Slang and Immoral Dances
There is no cost so dear as the price of slang and immorality seen enacted upon the stage by brazen, illegitimate performers, who vaguely think the applause of a few noisy rowdies is an endorsement that will meet the approval of managers who forfeit their pride and disregard the welfare of children for the sake of revenue only. The actor who swears too much is a nuisance. Some theaters don't allow it at all. But when it comes to smutty slang managers should not allow it: actors should be watched and chided and the limit of the law regarded. Stories that suggest ill repute are especially offensive. It is quite the same with suggestive dances. The shivering bodice, twitching of the shoulders, centralized emotion and balling the jack are all sufficient reason for the revoking of any manager's license.


[Note: the song BALLIN' THE JACK was published in October, 1913, only a couple of months before this article was published. The writer doesn't explain the expression "balling the jack"—he assumes his readers already know what it means, and that they understand why he considers it obscene.

[Furthermore, it is hard to believe that anyone would consider the song obscene, or the movements described in the song. Am I justified in concluding that the original meaning of "balling the jack" must have been something quite different from what is described in the song?—and that the song somewhat sanitized the concept of "balling the jack"?—JD.]