The south may have been aware of it, but they did nothing to resolve it. As a matter of fact they went decidedly in the opposite direction. The confed constitution (a cobbled up copy of the United States Constitution) included verbiage that specifically allowed internal slave trade (while prohibiting importation of slaves) and in 9.4 extended the explicit right to own other human beings in perpetuity.
The confed south did indeed "insist(ed) blacks be forever enslaved for the benefit of their white masters."
Righto.
Article I, Section 9, Clause 4
“(4) No bill of attainder, ex post facto law, or law denying or impairing the right of property in negro slaves shall be passed.”
IOW, the CSA built into their constitution a prohibition of emancipation. Presumably this applied to the CSA Congress. I don’t think they prohibited a state from freeing its slaves.