Your map doesn't go far enough. The Confederacy would have eventually acquired all the territories and many of the Northern states as well.
The economics would have made this happen. The South being independent would have broken New York's control over these other regions, and both the states and territories would have found it to be in their best financial interest to leave the USA and join the CSA.
So much for any possible suggestion that "the South just wanted to be left alone."
DiogenesLamp: "The economics would have made this happen. "
And when that didn't work, the Confederate army would make it certain.