Carex radiata might be a good option for these conditions if you want a low-growing sedge. Otherwise, you might want to check out Carex muskingumensis!

On my property, Carex pensylvanica is native. It grows all over in the dry areas, but in the wetter areas which include everything from damp soil to seasonal flooding, I don’t see it at all. So I think it wouldn’t be successful in your moist areas.