Eeek! Definitely green kallinga...I don't envy you one bit. Call your local extension office for suggestions on the control of this especially pesky sedge.

I say stiltgrass too, from sad familiarity with the little buggers. I have it in my gardens, not my lawn, so herbicide use is out for me. Here's a page from one of the invasive plant websites, with some recommendations for control. Good luck! Here is a link that might be useful: Stiltgrass

There's virtually no living turf grass in that area and there's nutgrass, so yes, start over. This is likely to be the month for you. Do you foresee much more heat this summer or will your evenings begin to cool down pretty soon? The problem was that you can't seed turf grasses in the summer heat. To kick this off, spray the area with RoundUp being careful with the overspray so you don't kill the rest of your lawn. Then start watering lightly (5 minutes), 3x per day, for a week. After the week you should have dead weeds and new sprouts coming up from the continual watering. Spray the RU again on the new sprouts. Give that 2 days to take effect and rake up all the dead stuff. If you want to use that same mix you can. Scatter the seed, roll it down with a rented water fillable roller, and start watering the same as you did for the weeds. This time you'll need to keep that up for a full month to get all the grass seed to sprout. Rye seed will sprout in a week, fescue will sprout in 2 weeks, and the KBG will take 3 weeks. So if you stop early you'll lose all that KBG. KBG will be the long term survivor in that mix, so you definitely want to get it going. That mix will keep you guessing as to when to mow. The rye will have been growing for weeks before the KBG even shows up. You'll have to endure the tall rye so you're not walking all over the KBG sprouts. After you have mowed 2 times it will be time to back off on the watering. You want to increase the amount but back way off on the frequency. Ultimately by the end of the early maturing process you'll be watering deeply once every week. This is only for new grass. Over the winter you probably won't be watering, but you could once a month. Then in the spring start watering once a month gradually increasing the frequency as the temps rise. When the temps are in the 80s you should have worked your way up to watering once every other week. Watering deeply means 1 full inch. Time your sprinklers to see how long it takes to get an inch. Put cat food or tuna cans around the yard and time how long it takes to fill them. Memorize that time, because that's the time you'll use every time you water. Watering like this will minimize weed seed germination, because it's the exact opposite of what weed seeds need. They need that daily frequency for the seeds to burst and take root.

I have lots of trees that interfere with my lawn; When I try to seed in the fall the leaves smother everything before it gets established and in the spring there are problems with other stuff the trees shed. its a constant battle. I did get some bluegrass sod down that looked really nice 2 years ago but then these seed pods started falling profusely; I can't explain how it destroyed it but it did. This is my last shot (I say that every year) but I'm worn out and haven't the money to keep doing this. Water is hugely expensive here having tripled in cost since I moved here.