I agree the heat in the South can be hard on food storage . However, the older homes were built on posts. The “old timers” and their dogs, along with other creatures, recognized that that crawl space under the home was a cool respite. Most of my relatives took advantage of this space by digging down into this space and using it as the closest thing to cold storage that they could get. Anyone living in manufactured housing has this same cooler space available.
I have used this space, just like the generations before me, for food storage. Sand is normally used in three-sided cribs for the root veggies and the 5-gallon sealed pails do fine there as well. I enclose this area now to keep out snakes, armadillo, and other animals but have housed food in this way for years without having any issues.
I also have an area where ferns abounded under trees with brush. This area, too, has been enlisted as a storage location. It is naturally cooler and moister there.
Get out and experience your property; there are probably places that fit your needs. – P.C.