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
I keep pointing out that they are siding with the King George position and not the founder’s position.