Hi all, I'm hoping someone here can offer some help, I'm at a loss after having searched far and wide.

Does sedgehammer kill herniaria glabra (aka rupturewort, aka green carpet)?

I planted a section of my yard with herniaria, but the nutsedge is still a huge problem after 4 weeks of constant weeding. The pic is after spending 2 hours weeding that small patch that you see....... The bigger problem is the nutsedge growing up through the herniaria I've planted, but a solution that will minimize the weeding between the plants would be pretty fantastic too.

Background - Zone 9b, new homeowner, front yard was overrun by weeds and gophers (have trapped 11 so far). I'm sure there are more weed seeds out there than grains of sand in the Pacific. Started out by spraying Roundup, tilled and amended soil, then planted the herniaria. Had no idea when starting the project that something as horrific as nutsedge existed.

Any tips, comments, questions appreciated. Thanks.