If you are using an auto door between the coop and the run, then I would not worry about using hardware cloth on the run, especially for a run that large.
Use hardware cloth to secure gaps around the coop itself. Sometimes Wayfair has good prices (and free shipping) on hardware cloth.
I lived right around there up until about a year and a half ago. Right on the Hwy, between Cumberland Furnace and Charlotte. We lost soooooo many chickens! From the neighbor's dogs, hawks and foxes, we lost the majority of our flock the first year.