It sounds like you have a pretty good setup and I really like what you're doing. I am doing something very similar in idaho on my property.
As far as groundcovers I would recommend planting a diverse mix of palatable perennial forbs, in what I would call a "wild game meadow". This will over time be invaded by some undesirable weeds and eventually transition to a forest if left undisturbed, but it will last much longer than a typical food plot. I would recommend looking at both warm and cool season perennials that do well in your area and I would use both natives as well as useful nonnatives. Some plants that might do well for you are Sainfoin, Alfalfa, American vetch, Chickory, Jerusalem Artichokes, Goldenrods, Perennial Sowthistle, Bush Clovers, Prairie Clovers, Milkvetches and Asters.
I have a blog that talks about this and some other similar topics if you're Interested. https://hunterseden.blogspot.com/2019/05/forget-food-plots-create-wild-game.html?m=1