Why? There was no abolitionist movement in the South to speak of. Even after the Emancipation Proclamation, blacks were treated essentially as peasants and indentured servants (like you said, pseudo-slavery). Jim Crow didn't start to crack until the late 1950's.
Slavery would have died out, but I could certainly see it lasting until the 1900's. The Civil War just moved the South from slavery to pseudo-slavery. No Civil War, and slavery could have easily continued for decades.
You'll recall the Germans reintroduced slavery in the 20th century in Europe. It's not that farfetched, especially in light of the Nazi-Southern connection. The only difference between Southerners and Germans is that the former is American, and cares more about money than genocidal ideology.
What? That Southerners are unapologetic about slavery? I can't tell you how many times I heard "oh it wasn't that bad", or my favorite "they were treated like family".
I mean hell, they're still unapologetic about Segregation. They're disenfranchising black voters as we speak.
Probably the weirdest one though was when a (Southern) coworker confided to me that he never realized how bad slavery was. Until he watched Django Unchained. I thought that summed it up well.
Southern culture glorifies the Confederacy, and sugar coats slavery.
I think what you're doing is essentially the exact same thing the South is doing in regards to the issue. You're absolutely right that many Southerners sugar coat their history regarding the Confederacy and slavery. It's a coping mechanism that allows them to ignore a lot of the ugly history as to the real reasons why the South seceded (slavery, not state's rights) and that their ancestors and homeland took part in something that was utterly atrocious.
But people who sympathize with the Union do the exact same thing to sugar coat the ugly things the North has done. By characterizing the South the way you do, it serves as a justification for the rather harsh treatment the South got for the Civil War and the aftermath of Reconstruction. It allows people who sympathize with what the Union did to ignore that the North was essentially the kid who kept on going "not touching you, not touching you" to the point where the South felt that they had to secede, that they too committed atrocities in the war, and devastated the South to the point where even to this day, they lag behind most states economically.
I say that it's absurd that slavery would not have lasted past 1900 is because in the end, humans are rational beings. They do a lot of stupid things......and I do mean a lot, a WHOLE LOT. But in the end, even those stupid actions have rational meanings behind them. Even though what the Southern aristocracy did was beyond horror and utterly atrocious in how they treated blacks and participated in the vile institution of slavery, they were still rational human beings. Even secession, as stupid as it was, as vile as it was because they seceded due to slavery, had rationality behind it. The vast majority of people aren't Calvin J. Candie from Django Unchained the way you're characterizing the South.
Now you are absolutely right that there really was no serious abolitionist movement in the South (there were abolitionists in the South, but their efforts were very small-scale in comparison to the movement in the North). But just because there was no serious movement in the South, doesn't mean that the wheels were in motion that spelled slavery's doom even without the Civil War. Politically, the balance was heavily in favor of the Free States because there was no place for slavery to expand to. All of the territories were going to become Free States because territories like Utah and New Mexico did not have the land to support an extensive slave system and territories/states like California, Nebraska, and Kansas choose to be Free Territories. Eventually the Free States would have completely outnumbered the Slave States to the point where they could have banned slavery. And slavery was ending around the world, peacefully due to various abolition efforts focused in Britain, the United States was not shielded by these efforts to end slavery worldwide. Hell, places like Brazil and former Spanish colonies, where slavery was far worse, ended slavery peacefully before 1900. Do you really think that a more developed nation like the United States, a nation of Anglo origin, which had far fewer slaves, would have ended slavery before places that had more slaves, were more dependent on slave labor, and had worse conditions? Probably not.
And economically it made more sense to end slavery. It would be absurd to expect that the Southern aristocracy would have ended slavery out of benevolence. But like I said, they were rational beings that could still see reason. Most of the Southern aristocracy would have eventually come to the conclusion that [poorly] paid labor is far more efficient than slave labor. Many would have been open to the idea of compensation, more so if Garrison didn't taint the Abolition Movement.