Slender rush control

Last spring we moved into our new house and had dormant sod that started to sprout well but was taken out by a late frost. After this the weeds took off better than grass for a bit. I was hesitant to use anything on them because the sod was so new and figured I would start fresh this year. We now have this grass/weed that started in the swale in front of the house that has now infiltrated much of the yard. I am fairly certain it is slender rush. It’s an absolute pain in the butt because it travels with rhizomes underground and the “leaves” are flimsy. I asked about controlling it at a nursery and was met with “pull each by hand” which at this point is an exercise in futility. Any idea how to get rid of it? Main grass is centipede, I incidentally have a crab grass problem as well but I cannot imagine I’m lucky enough that I could kill both with one product.