If your area allows it. Just seed heavy with fescue or zoysia. And keep it mowed once established. Those grasses will drown out the weeds over time if you keep it cut and don’t let the weeds reseed.
Hit it with one of several organic weed killers which generally have an acid base, and I’ve found that you get results within hours where they’re yellowing and dye fairly quickly. I’m finding that the organic based weed killers with the acid bases are more effective than glyphosate and based on some of the research seems to be safer.
Weedeat. Rake. Mow. Weedeat. Rake. Leaf blow. 2,4d.
Target 6.
Keep the little bermuda you have.