Given the elephant in the room, illegal immigration, that the "leaders" of our time will not utter in public, it's not that hard to believe that tariffs where the elephant in the room that the leaders of that time would not utter in public. If one is taking the ultimate step of armed rebellion it stands to reason that by then the gloves would be off and the causes for the rebellion would be clearly stated. And nowhere in the documents of the time is any reason for secession stated more clearly and more forcefully than defense of the institution of slavery. But there were some discussion on tariffs. Alexander Stephens, for example, spoke on tariffs in December 1860.
"Yes, and Massachusetts, with unanimity, voted with the South to lessen them (tariff rates), and they were made just as low as Southern men asked them to be, and those are the rates they are now at."
What you say makes sense, but the ancients in my southern family related the war as being more about Northern aggression than slavery. In fact it was called the War of Northern Aggression. They say the man on the street usually couldn't afford a slave, nor did a majority of Southern families have slaves and that the war was based on taxes and slavery was merely the excuse.
I don't know if that is true or not, it may just be what was passed down to them. I tend to trust the accounts of those closest to the event given how lately history seems to be rewritten to suit the agenda.