I think we have to draw a sharp distinction between antebellum and post-war Southern economy.
Post-war everything you say is doubtless true.
Antebellum is a much different story.
Perhaps I can explain it this way:
In 1860 the US Deep South was the Saudi Arabia of cotton -- the world's largest, cheapest and most profitable mass producer of the most important global commodity, industrial grade cotton, and had been for decades.
Since the 1840s the world had beaten many paths to the South's doors, demanding ever more cotton at ever higher prices, and the Southern economy grew like crazy to meet the demands.
And along with its rapidly expanding economy grew its population and prosperity.
Yes, Tara from Gone With the Wind was somewhat above "average", but it certainly represented Southern aspirations.
Note that Southern railroads were intended foremost to take product to ports for export, and Southern products represented at least half (some claim 3/4) of total US exports:
So far from being some kind of backwater, in 1860 the South was a prime driver behind overall US prosperity.
You can also see slave ownership declined dramatically the farther west you went in Texas.
Kansas was not suitable for plantation agriculture or the ownership of slaves in any numbers. The only reason the slavers wanted it was to get two more Senators.