Gordon's Empire of Wealth: The Epic History of American Economic Power (P.S.) notes that American cotton was unknown at the time of the collapse of the indigo market.
Indeed, so little was grown that when a bale was exported to England in 1784, the first instance of cotton as an American export, it ran afoul of British navigations laws. These laws required that raw products arrive in British ports either in British ships or in ships of the country of origin. Customs officials simply refused to believe that there was such a thing as American cotton, and the bale was left to rot on the docks of Liverpool. [pg. 83]
Cotton was grown in America, but not in large quantities, and not for export. What changed was the land on which the cotton was grown:
But there was a big problem. Unlike Sea Island cotton, the seeds of the upland cotton are sticky and cling tenaciously to the fibers that surround them. Separating the seeds from the lint, as the cotton fibers are called, was in immensely time-consuming task. While a field had could pick as much as fifty pounds a cotton bolls in a day, it took twenty-five man-days to remove the seeds form that much cotton by hand, a process called ginning. [pg. 83]
With a worker, you pay them incrementally for their productivity. With a slave, you are largely paying in advance for their productivity. Either way, when their productivity goes up, so does the going rate:
Cotton changed all that. After 1793 the price of a slave ratcheted upward. A slave who would have sold for $300 before the cotton gin was selling for $2,000 and more by 1860. The slave holders, possessed of an increasingly valuable asset, were less and less inclined to part with what became, in the early decades of the nineteenth century, an enormous capital investment. [pg. 87]
Many find it offensive to think of people, in the forms of slaves, as capital. But, the key to understanding capital is that it is a productive asset whose depreciation risk is carried by the owner, whereas with labor, the depreciation risk is carried by the worker (as many men in unskilled physical labor jobs find out in middle age).