It's a unique situation but I had an ~ 8' x 3' raised flower bed with some rose bushes that I wanted gone. Under the roses was completely full of nut grass. After I chopped the roses out, I went after the nut grass manually. I'd dig up the bed down to 6 or 8 inches depth. I'd pull every nut and runner out that I could find. A week later, it was growing back, but thinner. I'd repeat the process. In about a month, the nut grass was all gone and I planted some new shrubs (through slits I cut in the weed cloth I laid down first.)
I had a a clear space and no time crunch, so that worked for me. It was good therapy, I got to take my frustrations out on that damn nut grass!