Though no one wants to spend more money with corn commodity price so low, it will pay off next spring to have less Palmer amaranth to control in soybean or cotton. With the rain the first week of August, any thin corn stand areas will likely have a heavy flush of Palmer amaranth.
Good options to control this late flush of Palmer in Tennessee corn include tillage and the burndown herbicide Gramoxone (paraquat).
If you elect to go with tillage, a disking will likely provide good control of smaller Palmer (<4”) but larger Palmer (>8”) will often re-root and grow back. Likewise, Gramoxone will provide consistent control of smaller Palmer but regrowth can happen with larger Plants.
Residual herbicides should be considered as well with so much growing season left. Fall applied residual products like Sharpen, Valor, Dual Magnum, metribuzin and simazine would all be good choices here, depending upon what crop is to be planted next spring.
Sharpen is probably one of the more versatile residual options as wheat can be planted anytime after the herbicide is applied. Sharpen can be used at rates up to 2 oz/A in the fall before wheat, corn, grain sorghum and soybean. Valor could work as well if corn harvest is early as there is a 30 day plant back to wheat after a Valor application.
Other residual options can work as well like Dual Magnum or metribuzin if the fields will go to crops other than wheat this fall.