How about the people that actually WERE slaves get together with the people who actually OWNED slaves, and they can work it out amongst themselves? (Assuming there are any of either population living now, of course.) If you weren't born a slave, and you haven't owned any slaves, then other than remembering the mistakes of the past so as not to repeat them, the Civil War isn't really relevant anymore.

If we're going to punish people for the mistakes made by their ancestors, then we might as well start the punishing with, well...everyone. Everyone has ancestors that did bad shit, so should we all go through life flagellating ourselves for the misdeeds of our ancestors?