Hmm there are two different things going on here. 1) Discussions on how the North handles the issue of African-Americans 2) Discussions on how the South will deter slaves escaping. While the two are connected, they are two different Alternative History topics
On (1) I find the idea of any support for an international fugitive slaves act problematic. And while local governments can muck around, I cannot see the Federal Goverment letting them do so. A lot will depend on how the North decides to handle the issue. It is not monolithic, but so was racial prejudice and legalized racism not monolithic. As long as there are states in the USA more willing to give African-Americans a chance, there will be little reason to interfere with escapees beyond funneling them towards those states. The Federal Goverment could decide to resolve the issue partly by a reservation policy as it did with Native Americans, it could also go with the historical results of the Constitutional Amendments. A lot will depend on when the war ends and how. 1864 with a McCellan-Pendelton Presidency? Very hard to see any willingness to play along with the South on this. Hard-liner attitudes of weaking even an Independent CSA would lead to tolerating the Underground Railroad. It could more seriously support emigration to Canada or Africa (with the US perhaps taking a much more serious interest in Liberia). A lot will depend on whether you still get Lincoln's favored policy of letting the border states do emancipation and when they do.
The point is that even a Democrat victory is not going to implement the Chicago Platform.
What I am trying to say is that while many Northerners were racial prejudiced, and many Union states racist, there was a general deep seated opposition to a) expansion of slavery b) that morphed in the crucible to war to opposition to slavery. These are not going to go away.
My view is that the general idea would be to "encourage" escaped african-americans to emigrate or move to territories (and let those territories figure things out perhaps violently). Racism in the USA might interestingly end up with at least one majority African-American state carved out of territories (why not, the LDS got Utah). Since the US African-American population will not be as big as it was OTL, a state would not be totally weird, and one easy way to resolve this for the USA.
I would thus caution against an assumption of a seamless coordination between the slave-holding CSA and the slavery hating USA on this issue.
That said, there are of course multiple ways for the CSA and CSA states to alleviate the loss due to escapes. This will range from police power repression to schemes of gradual emancipation that would keep many slaves put in the hopes of liberty for themselves or their children. Remember the CSA constitution only says the CSA goverment cannot abolish slavery. And you could have state constitutions that de-facto abolish slavery but not de-jure. Politics is the art of the practical.
What I do not see happening is the CSA stirring the hornets nest again by too aggressive an attitude over this issue vs. the USA. A CSA that eschews expanding slavery on the continent, and avoids antagonizing the American System as seen by the USA (refer to McDougall) can get away with a lot more than a CSA that picks a fight over territories or goes on some stupid adventure in Central America.
Again a lot depends on the contours of a) how the CSA becomes independent b) when
That said my view is that chattel slavery as practiced in the ante-bellum south was not going to survive long. But again , as long as you keep the de-jure rules, there is a lot of leeway what you do de-facto.
And the same goes for the USA.
That said I do think the Great Migration still happens. Indeed it might even be a coordinated policy between the USA seeking labor to replace people marshalled for WW1 and the CSA seeking to alleviate its own racial issues. Interestingly though the migrants will be CSA nationals, and thus you might get a situation similar to Gestarbiter in Germany, or Koreans in Japan, in the USA.