I might actually have an idea on how the Confederacy would return.
During the American Civil War there were members of the Confederacy that formed a group called The Knights of The Golden Circle. A secret society. Conspiracy theory has it that they managed to steel a lot of Gold and such in order to rebuild the Confederacy.
So have it so this Society never actually died. It died. Sure over time its members might have stopped taking the idea of rebuilding the Confederacy seriously but kept it going as a social club. As things in America started to fall apart leading up to the Great War. The some members started to like the idea of forming a new country and looked to their founders and an example. They build themselves shelters maybe with the Confederate Gold and survive the Great War. From those Shelters they set out to form their own nation based on what they thought made the Confederacy Great.
A note. The Legion aren't trying to rebuild the Roman Empire. Caesar is just using what he thought made Roman Great to his advantage to build his new Empire. The Minute Men like the concept of helping people like the Minute Men of old. I don't recall them trying to rebuild Colonial America.
Anyways if you want an actual return of the Confederacy or something every close to it, than the Confederacies https://en.wikipedia.org/wiki/Knights_of_the_Golden_Circle might be the way to go.