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Your analysis is flawed for several reasons.
Prior to the Civil War there were few "southern debts". The production of cotton was in those days as great a cash cow as is the production of crude oil is today. In fact, a great deal of the capital held in New York City banks was owned by Southerners, and several banks in NYC almost went under when Southerners withdrew their cash at the beginning of the War.
Many slaves escaped to the North, but as a percentage of the total number of slaves, the escapees were few. One must remember that almost all slaves were illterate and had no conception of what or where the North was, except as a place "somewhere up there."
Indeed, even if they had known, the difficulties of traveling hundreds of miles through territory swarming with slave catchers were almost insurmountable. Even in Kentucky, the slave state closest to freedom, few slaves fled to Ohio.
The importation of slaves into the United States had been illegal since 1807 (I think the date is correct) and slvaes knew no other country other than the US and no status other than slavery.
The Romans had a saying that it took three generations to make a slave - meaning, of course, that after three generations a slave has no memory of freedom - and by 1865 most slaves in the US had been chattel for far longer than three generations.
I doubt that war would have broken out over access to the lower Mississippi. It was in the interest of everyone, particularly Louisiana, to allow commerce to flow freely along the river.
Texas was the Southwest in 1865, and it had known and defined borders. Oklahoma was Indian territory. Arizona and New Mexico did not exist except as geographic entities. The rest of the West, with the exception of a few scattered settlements in California, was nothing more than a blank space on the map; the Great American Desert most of it was called.
Why, indeed, would war have broken out? A settlement of the dispute between North and South was in everyone's interest, except the slaves.
I doubt if you could have convinced Iowa, Illinois, and Michigan farm boys to march south to free the slaves; save the Union, yes, but free the slaves, never. Certainly, the Irish of New York would revolted rather than undertake a war to emancipate a labor force that would have competed with them. THE GANGS OF NEW YORK, the book not the movie, details the hostility of the Irish toward black people.
Again, I beleive that a political deal short of secession was possible; some sort of federation between the two sections of the country is the most likely outcome. Thankfully, it did not happen, for if it had, slavery would have lingered into the 20th Century.

Thanks for the thoughtful post, but fighting between the USA and CSA would have dragged on and on -- where to draw the border? would the USA tolerate CSA oppression of Unionists in Appalachia and the Ozarks? which side got Kentucky and Missouri? would Louisiana charge tariffs for goods flowing down the Mississippi (many wars have been fought for far less than that)? you think that slaves would not flee north once the USA was no longer obligated to arrest fugitive slaves and ship them back? you can't imagine why the CSA would covet California and Arizona?

Your analysis lacks an appreciation for reality if you really believe that "a political deal short of secession was possible; some sort of federation between the two sections of the country is the most likely outcome."

That makes no sense at all.