The problem was that it was just not about slavery continuing to exist where it did. The slave states, particularly those that did secede, saw that even under "popular sovereignty" you weren't going to see an expansion of slavery, and that in some slave states it was clear that it was in the way out. Fighting against "liberty laws", which many states enacted which said a slave who set foot in that state was free, the fugitive slave act, and continual attempts to redo deals about where slavery might become legal in territories all show it was not about allowing slavery where it existed but guaranteeing it everywhere. After all, in theory, if slaves are considered protected property, there is nothing to prevent somebody moving "north" with a bunch of slaves and setting up an agricultural enterprise using that labor, even if that state is a free state.
"No bill of attainder, ex post facto law, or law denying or impairing the right of property in negro slaves shall be passed" (Constitution of the Confederate States of America) This makes it pretty clear how important the CSA thought slavery was.
Even with the 3/5 clause the south had pretty much lost control of the House of Representatives by 1860 (57/241 representatives were from the states that seceded, 24/241 from border states that still had slavery but did not secede). In the Senate there were 17 free states, 4 border states, and 11 slave states who seceded. The reality was that no new slave states were being added, the old compromise of one of each being admitted was falling apart under demographic and economic reality. The legislative balance had turned against the slave states, and was only going to keep going in that direction.