The funny thing is that Lincoln pretty much said they could keep their slaves for the sake of keeping the union together. He had made it clear he wanted to abolish slavery, but he wasn’t going to risk the nation over it. He basically opened with an offer to let the south have everything.
The South, however, believed that the day would come where the US would abolish slavery, and they needed to get out before that happened.
Given the South were handed everything they wanted in the default position, no amount of negotiation would have worked.