Allow me to commisserate with you....
Here is my ongoing battle with chufa, nutsedge. Hmmm... looks like I need to update the thread.
Shorter cliff note version:
I tried wood chips to smother them. They got stronger. But easier to pull as the woodchips broke down.
I have and continue to excavate various small areas, pretending to be an archeologist. I have a wooden form with 1/4 inch hardware cloth stapled to it, I get a shovel full of dirt, and use the form as a sifter, pulling out the chufa to be destroyed.
Cover the area with a tarp to solarize the area for several months. I did mine from April to late September.
Follow up with grasses, tall cover-crop to choke out any leftover nutgrass/sedges. My fight is ongoing...
I think in your case, sifting the soil might be successful after the solarization is done.