If money weren't an issue, or if you could find both of these things in quantity for cheap, I would layer
compost on a large scale using ramial wood chips from urban tree services and cattle/horse manure. Or, for ease of application, work them in windrows, perhaps tarps over them, and make sure there are lots of red worms and Black Soldier Fly Larvae. It could be done. I would like to know what BSFL and vermiculture do to persistent herbicides, because I know that heavy metal counts go down after worms pass through, for the reason that getting that amount of manure from organic sources would be rough.
But to make my point clearly, if carbon breaking down is your main problem, many tree services companies where I live will deliver ramial wood chips for free if you ask for enough of them. It's a waste product for them.
Or you could build a biochar kiln and get woodchips (if you can, I don't know where you are), and make really high-quality ammendment that will build soil structure and not break down. If I don't know what the most biochar you would want to use in terms of a ratio with your topsoil would be, but you could directly increase the your volume of topsoil and its structure that way.
-CK
A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.
-Robert A. Heinlein