Your problem is the chicory and these are always issue with combo plots. Short answer, spray mix of Cleth and 2,4- DB which will take care of most of issues but probably kill the chicory. It is easily reseeded tho thru May is if you want to recoup.
Personally I spray Cleth and mow weeds as they start to flower, removing at least the top 3-4 leaves of growth. Spot spraying of stuff like thistle with gly takes care of that problem. There are no easy cheap solution with the mix of plants otherwise. Make sure you never apply N with Fert application as that promotes the problems. And as alluded to, grasses should be 6 in or less and actively growing for good success. You can mow then give week or so for new growth then spray. Good luck.