“than in the Upper South, whose states did not secede until after Fort Sumter),”
Ft Sumter isn’t what prompted the Upper South states to secede. They seceded in response to Lincoln’s April 15th call for 75,000 troops to force the Deep South back into the Union.
Had Lincoln been patient instead of eager for war the Confederacy would have been smaller and not likely to last long. Instead his call for war resulted in a much larger and more powerful opponent.
His call for troops was in response to the South starting the war. Lincoln didn't start it.
I don't know if further delay would have changed the outcome--unless Lincoln called for troops secession of the Lower South would have remained the de facto reality, and if he allowed Fort Sumter to surrender because of lack of provisions the demoralizing affect of that on the North might have caused the attitude of "let the erring sisters depart in peace" to become even more widespread. Whenever Lincoln showed his hand that he would use force to coerce the seceded states back into the Union the Upper South would have been forced to decide whether to secede. Besides the four which did secede, two others (Kentucky and Missouri) struggled with the possibility.