Indeed, slavery likely lasts into the 20th Century without a Civil War.
That's an even bigger stretch than my own interpretation, particularly with the advent of the industrial revolution.
Many areas of the South were hardly touched by the Industrial Revolution, with the exception of cotton factories. I could also see slavery lasting about several decades longer than it lasted in RL, as the South was very slow in changing it's ways and traditions. In fact, I could see slavery being abolished during/after WWI in this scenario. Women got the suffrage in RL due to their service in the war effort. If slavery was still around, I could see blacks getting more rights after WWI also as a sign of appreciation for their wartime service.