I think your assessment is spot on. I have concluded that even if you could transport DiogenesLamp back to South Carolina in 1860 when they seceded he would argue with them that their not really seceding because of slavery.
Didn't they already have it? Wasn't it already part of the Union for "four score and seven years?"
Even so, it is irrelevant why they left. The principle articulated in the Declaration of Independence assured them of the right to leave whenever they believed the existing Government no longer represented their best interests.