I think you have the economic history of the cotton gin backwards there. The slave economy was much more tobacco-centric before the cotton gin, because even with slaves, cotton was too labor-intensive to be worth large scale agriculture before the cotton gin. The cotton gin is a good example of Jevons paradox, where making something more efficient (in this case, making cotton harvesting more labor-efficient) ends up increasing demand (in this case, of cotton-harvesting labor).