I live in the northern tip of South Carolina and I have the same issue. I planted sedum but they didn't keep the weeds out and they seem to grow too slowly to crowd them out even if they would once they spread. I've had some luck with ice plant. They spread pretty quickly but don't seem to be invasive. I've also found them to be fairy drought tolerant in my area. I never water them and this summer we were in a drought from early July until really present and they are still doing good. Purslane will grow quickly and spread quickly (and it's gorgeous) but it is invasive here. I had some of those in hanging baskets only and I've been pulling them out of my flower beds, on the other end of the yard all summer. Good luck! I'm going to follow this thread and see what ideas come up.
