So, I live in Louisiana and the main problem here is that the grapes have too easy of a time here.
They just grow really big and juicy, so you've got a lot of water, a lot of sugar, and comparatively thin skin, so fewer of the compounds that make for decent flavor. Generally speaking, we are probably better off just helping folks in Arkansas make a decent product. Local is a relative term, and, at least some regional specialization is probably a good idea.
But, here are some ideas. First, the smaller grape varietals are probably best. We need varietals that have more skin when compared to their moisture and sugar content. Second, grow the vines in harsher areas, and in some cases, plant competitor species. I don't know how often one would actually have to plant competitor species, but there would also be a lot of complementary species around, hopefully, because farms should be a poly-culture.
Then there are techniques like what the Italians do when making Amarone they let the grapes dry. It reduces water content and concentrates sugar and flavors. A high-alcohol yeast ought be able to take care of the higher sugar content during fermentation.
Another interesting area of research would be the vessels in which they are stored. We have a lot of red clay in our area and it would be great to see what kind of character fermenting and perhaps ageing the wine in vessels made of such clay would impart.
The limitations presented by the land and climate combined with learning about regional traditions in similar regions can serve as a jumping off point for creativity and innovation.