Your argument against secession broke down, but not until your first sentence.
By your own account, the Union states were obligated to amend the constitution using the amendment process if they wished to prohibit secession.
Secession was certainly not prohibited in the constitution then, or now.
And per the 9th amendment, it was not necessary for secession to be enumerated as a state's right in order for it to be available.
You need to revert back to that tried, tired, and hard-to-disprove argument: God told Abraham Lincoln to destroy the South and kill all those people.
I already quoted your leadership's beautiful, stirring words, above.