Pretty sure Sedgehammer (google a few varieties or combination herbicides & read labels) will do it in. Clethodim & crop oil only kill TRUE GRASSES. Sedges are different. Hence, using Sedgehammer herbicide.
Next: stay on mowing as well - herbicide is what you want to - to fry it - but, mow to insure more doesn't go to seed as another minor tool.
Last, if no success.... Glyphosate. Heck, even at a qt/acre, gly doesn't kill my clover. geesh, I think I've tried 3 qts and doesn't kill it
. NOT suggesting that!!!!!! But, if a guy wanted to throw .5 qts of gly on well established clover, be ok most likely. Or - spot spray the sedge with heavier gly. When I had more time, every time I went to my clover plots & sprayed - I'd scatter a little more clover here and there. Did it help? Sure, sometimes. unless drought and hot. Did it hurt? NOPE, just a few bucks to spread a lil here and there.