Like any divorce, the South (Congress) should have taken its case to court. There the terms of separation could have been hammered out without resorting to violence. Probably could have been accomplished in less time than it took to fight a war...and certainly with less blood and treasure expended.
And if no settlement could be reached, then at least the South could say it tried to resolve things peacefully first.
It's not mentioned in the wikipedia piece but one problem with such proposals was that Lincoln was never going to do anything that equated to recognition of the Confederacy, so he refused to meet with them.
Lincoln's position from day one is that the states had never left the union; they were simply controlled by rebellious men. His position was remarkably similar to what King George had to say in 1775: A Proclamation For Suppressing Rebellion and Sedition