Most CSA Victory! timelines have a way to optimistic slavery end date.
So there's a problem people will run into with the "The Lost Cause Victorious!" timelines, and its that because most of us have at least some of the moral compass of 21st century individuals, the CSA has to show that yes, it was really about state's rights and not founding a society on the enslavement of other human beings. This even goes for "The Lost Cause Victorious II: Trent Affair Buggalloo" timelines, because the British Empire that lasts well into the 22nd Century can't have a Southern ally/client state that is fond of slavery.
The biggest handwave is the Bull Weevil. It makes cotton production less dominant, and thus the free market will take away slavery. This generation's Lost Cause tends to be very Ron Paul, Austrian economics inflected, so the Bull Weevil is quite popular right now. The problem this runs up against is... the free market. And here I'm talking the free market of Adam Smith and economists, not the free market that will solve many problems while requiring no money from you, or the free market that would inevitably turn you into John Galt if there were less regulations. It runs up against many cultural, political factors - but also the plain free market. We're talking about plan simple market forces here, and how they affect wages, and labor, and all sorts of things. Because, you see, it was about more than just cotton. The slaver aristocracy was diversifying - rice, indigo, and many other crops were grown with slave labor. In addition, by 1860, the aristocracy was diversifying into industrial concerns - brick making, iron working, etc.
But M. Stuart, you say, don't you know that unfree labor is less economically efficient than free labor! And yes, I do know this. In terms of large scale economic output, it is. But for your individual slave holding capitalist, it isn't. You have a labor force you get to give the ruthless bare minimum of clothing, food, and shelter too. Again, history back me up. Wages for whites outside of the slaver aristocracy were much lower in the South than the North - this is simple economics. You cannot negotiate for higher wages when the other person has the option to replace you with... someone who has to work for next to nothing. Probably affects the price you sell at too - as is the case today, people don't give a shit about how it was made if they can get it cheap. By 1860, the aristocracy is diversifying out of cotton, and while that would lead to an industrial South which would produce less overall than a free South, it will make the slave aristocracy fabulously wealthy - no cotton needed.
And lastly, for all of the sentimental, hazy filtered nostalgia of a rural society with manly, rural values resisting the encroachment of the grimy industrial North - this was a feudal society. Large landowners called the tune, and expected deference. Why do you think that Lee's soldier called "Marse Robert"? He was one of their beloved lordly class, and "Marse" is what you said - free or slave alike. The Southern slave holder as kind master over his flock is at the heart of the elite's conception of itself. As mentioned above, it is written into the Confederate Constitution. They viewed themselves as a feudal aristocracy, to the point where they even staged the occasional tournament in the 1850s (look it up). They are not going alienate the core of that feudal identity, especially as it kept them rich. And as the 19th rolls to a close, eugenics and Social Darwinism will only cement this conception, not challenge it.
The short version? Your 21st century values are what demands a victorious CSA get rid of slavery as fast as possible. Their 19th century values made no such demands on them. And an actual historical timeline most acknowledge that people in that time will make decisions as people in that time, not decisions to make you feel better.