I was thinking about the Liberia idea mentioned in the thread and I cannot see it making sense for CSA still committed to maintaining slavery. Such a big free Confederate-African population can only arise due to manumission on a big scale. And the slavecracy knew even before the Civil War that manumission is as a big threat to slavery as runways. Most slaveocracy dominated states had made manumission impossible exactly for this reason. Instead I think the colonization project will be a tool used by the USA to manage runaway flows. I can see more anti-CSA USA administrations preferring to dump runaways in Liberia rather then deporting them back to the CSA, wile more pro-CSA USA administrations preferring deportation back to the CSA, so it will ebb and flow but might become the preferred option as time passes. The evil genius of this is that it will still likely depress the number of runaways because many will not want to risk it if the result is deportation to a far away and alien place.
I think the tipping point is when the brookahs come to the conclusion that the only way to bring down the slavocracy in the CSA is to undermine the institution. It is then that we will see border state governments start doing things like making manumission easier, and it is then that I expect the underground railroad to become truly massive. And it is then that we will have a serious constitutional crisis in the CSA as the deep south states will try to use CSA federal power to stop border states from doing that. And it is then that we will have the same with the USA. Abolitionism will turn to a point of opposing deportation to Liberia, because that undermines the effect of border state manumission. That is the point of infection. If you get easier manumission in the Upper South + USA permission of free states and runaways to stay in its territory, slavery is dead. Except if the Lower South makes the intra-CSA border a hard border. This is why I cannot see how you avoid a Estado Nuovo style authoritarian regime in the CSA down the path. The Deep South needs to control the ability of Border States to end slavery in their own jurisdiction due to the possible domino effect. They need a slavery accommodating USA, they need states not being able to make manumission easy, and they need hard borders with Mexico and the USA.
And mind you this does not require some moral change among racially prejudiced whites. They will just come to their own conclusion that it is in their interest to smash slavery as an institution. The slavocracy knows it cannot survive if border states do not participate any more in propping up the system. Hell you do not even need runaways. Just abolitionist societies buying large amounts of slaves, moving them to a border state and then manumissioning them. Still though a lot depends on what those borders states do with the freed now Confederate-Africans and what the USA does.
An interesting question is the role of the Mississipi here. Depending on the regime of internationalization, if i.e it prohibits search and seizure of boats while they are not in port, it will become the main route of the underground railroad.
So the political economy of slavery points to its downfall. If brookahs want to break the planter elite they have to break slavery. Breaking slavery can take two forms, assisting runaways + making manumission easier. But both these require a sympathetic USA that does not enforce deportation (either back to the CSA or to Liberia). There is no way the lower south lets the upper south put the institution on its death path there. States rights be damned...and you all know what that will mean.
That is the dangerous alliance for the CSA elite structure : white brookahs determined to break the planter elite + slaves seeking freedom + northern abolitionists determined to change USA policy. The moment the USA decides to stop propping slavery in the name of racism is the moment planter elites will see the writing in the wall.