Hey there, welcome to permies!
I live in Meigs County, TN, not sure which county you are in. Red Clay is the norm around here.
How quick are you looking to get the soil fixed?
You could gather the leaves from the back side of your property for a couple of seasons, shred them and compost them and after you have a good amount of leaf mold spread it over your soil.
You could also obtain sawdust, usually free if you are willing to pick it up from a sawmiller, and manure from a cow/horse/pig farmer to create a nice back to eden type soil over your bad spot.
Another approach would be to just create large compost piles with manure, grass and sawdust for a few seasons and spread that over your area.
If all that doesn't sound appealing, you could haul in topsoil from somewhere else to cover it.
The last resort: