I live in the eastern part of North Carolina, so I don't know how well these would work for where you are but...
Wild carrot A.K.A. Queen Anne's Lace will outcompete the grass for sure (if it can grow in your area that is..). I've added some as well as wild mustard and domestic plants like chamomile oregano & mint all over my front
yard to reclaim it from crab grass.
Clovers, sheep sorrel, & catsear (false dandelion) also find their way in help build the soil and attract pollinators!
Every part of the wild carrot can be used medicinally by making tea, and the young
roots are also edible and pretty good.
Cheers