The South NEVER had any designs on Conquering the North and overthrowing the Lincoln Government. As far as they were concerned the North could go it was and do what they wanted to do. If they wanted to free their slave the South would not have interferred with their politics. But, a simuliar attitude was not in Lincoln's thinking. His answer was to try to force the southern states to bend to his will.
You will notice that the cost of war was too expensive, so he offers to BUY the Slaves? When if he just allowed the Southern States their Independence It would have cost him less to withdraw his troops. He had no intentions of doing that.