Berkley sedge (C. divulsa) Will probably do full sun where you are. It survives in my central Texas garden in Part shade un irrigated. I think it would be happier with a tad more water, but hey this is Texas. I am just happy it is alive. Cedar sedge( C. planostachys), Texas meadow sedge (C.perdentata), Texas sedge ( C. texensis or C retroflex sold as Scotts turf)). I have a beautiful bright green long sedge that grow natively out in the rocks in the sun on a hill without irrigation. It is different from my Cedar sedge but I am no sedge expert. I have tried growing it from seed, but so far, no luck.

Carex brevior grows in full sun too

Just a follow up to this, last fall I planted landscape plugs of Sporobolus as a matrix. I'll give update later this summer.

northraleighguy , any update?

I realized that native carexes would not survive well, on a slope, in full sun in 7b. I really needed a grass instead. So I planted sporobolus and this will be the second growing season and so it will take a while for them to fill in. They're not kidding when they say they take a while to establish. But the roots are deep and they're excellent on this slope where I hope they will help control erosion. They and calamintha are the matrix plants in a large planting of echinacea purpurea, aster oblongifolius, liatris, allium 'Summer Beauty', stachys officinalis, agastaches, etc. The fine grassy clumps in this picture are sporobolus. I'll try to update this as it fills in.

@northraleighguy any updates?

This is a difficult hill for which to select a matrix plant. It is on the northwest side of my house, and once you factor in the shadow of the house, parts of the hill don't actually get a full 6 hours of sun. So it's barely enough for some grasses, and yet some sedges (like carex appalachica that volunteered) trend to get burned out.

The sporobolus died off. Not sure if it was because I planted in the fall, which I'll never do again for a warm-season grass. But even the ones that lived were scrawny and never got to a large size in over two years So now on the shadier parts of the hill I'm using a sedge I found in the woods (I think it's c. pensylvanica), and on the sunnier parts I'm using a muhly grass that is smaller than the typical pink muhly (Muhlenbergia reverchonii 'Undaunted'). So far so good on both. Given the fairly steep slope with erosion, and challenging light situation, and constant deer and rabbit predation, this is the toughest area I've ever had to fit plants to.

Yeah, fall plantings of native grasses tend to not overwinter for me either...and it requires basically full sun (prairie dropseed).