Challenge: How could the CSA peacefully return to US, starting in Lincoln's term?

Inspired by Codae at another thread.

The Confederates don't fire on Fort Sumter. When Jefferson Davis has a fatal heart attack (due to butterflies), agents of Lincoln support a pro-Unionist for Confederate President. The CSA uses this a provocation for a war against the USA. Great Britain and France, figuring a divided America is a weak America, support the Confederacy, but south America is reabsorbed into north America. This is considered the first "modern war".

Now, how could the first part of this come around? Make it so that the CSA, despite declaring secession, has a Unionist leader come to power during Lincoln's presidency, with at least an eventual reunification. Most any PODs are allowed.
 
If the Confederates do not start the shooting it would be hard for Lincoln to start it and retain support.

As I understand it several states, crucially Virginia, had not made up their minds. If Virginia eventually decides to accept the lawful government of the US

This might leave the Confederacy a 7 state rump.

Oh and the US could insist that Fugitive slave laws did not apply to states failing to accept Federal authority.

I think Stephens, the Confederate VP, might have been inclined to accept some kind of deal

However I wonder how likely such a CSA President is to have been shot.
 
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