"After 620,000 had perished, the issue of a state's right to secede was settled at Appomattox. If that right had existed, it no longer did."
You're confusing might with right. Might does not make right in this case, it just makes for tyranny. The right still exists, just as it existed in April, 1865. The might still rests with those in control of the "Federal" government. Secession won't happen in modern times because very, very few are willing to die for liberty in this day and age.
"When in the course of human events it becomes necessary for one
people to dissolve the political bands which have connected them with
another ..."
So begins the Declaration of Independence of the 13 colonies from the king and country to which they had given allegiance since the settlers first came to Jamestown and Plymouth Rock.
The declaration was signed by 56 angry old white guys who had had enough of what the Cousins were doing to them. In seceding from the mother country, these patriots put their lives, fortunes and honor on the line.
Four score...
might makes the victorious side right, whether they are or not.
The Constitution does not have an anti-secession clause. And it does not somehow trump the inalienable right to self-determination spelled out in the Declaration of Independence. Furthermore, there were states (at least Virginia and Rhodes Island) which explicitly reserved the right to withdraw from the union when they ratified the Constitution. You simply do not know what you are talking about.
And, for all you have heard about the War of Northern Aggression being about slavery, it just isn't true. Primarily, it was about taxes and Lincoln's plan to use southern taxes to pay for northern companies.
I am not saying that slavery was not an issue with some people, but it was not the big issue you seem to think it was.