The real problem in 1860, just as in 1856 (and today!) is that Democrats hate, hate Republicans and go crazy when real Republicans (as opposed to RINOs) get elected.
In 1856 Southern Democrats threatened secession if Republican John Fremont was elected President -- was that because Fremont wanted higher tariffs?
Nooooooooo… it's because he opposed slavery.
So Democrats won in 1856 and forgot about secession until... 1860 when Lincoln became their new devil and once again Southern Democrats threatened secession if Lincoln won -- because Lincoln wanted higher tariffs?
Nooooooo… because Lincoln opposed slavery, however mildly & tangentially, it didn't matter to Fire Eaters.
"Ape" Lincoln was a credible abolitionist devil they could use to whip up anti-Union pro-secession sentiments.
DiogenesLamp: "Lincoln was even desirous to make it even more legally protected than it already was. (Corwin Amendment)"
The Corwin Amendment rose from proposals submitted by senators like Jefferson Davis, intended to mollify Southern fears of abolitionists.
Lincoln's view was that it changed nothing really, so was acceptable, but he did not sign, support or promote it.
It got only four ratifications.
The 13th Amendment which Lincoln did support strongly was passed & adopted into the Constitution in 1865.
You do realize that the Republican Party was the liberal party and the Democrats were the conservative party in the mid 19th century?