Slavery in the South, whether legal or not, would not have persisted long past the turn of the 20th even if "The Cause" had prevailed. Follow the money.

As with Brazil and the other "late" slavers, the economics of slavery simply didn't work after the introduction of the internal combustion engine. ICE tractors and the like were simply too efficient and the marginal cost too low for too many tasks -- even in market agro environments. Slavery rapidly becomes economically unviable. Moreover, the infrastructure for an ICE economy requires at least a smattering of education among a much higher percentage of the work force, again making the planation economy difficult to maintain and inefficient.