You can leave the dead grass. It will shade the soil. If it gets too hot, you won't have any worms there and they will help it all recover. You could put down some humus mix or Dillo Dirt on these spots to help reactivate the good bacteria that the chemicals have killed. Keep it watered and direct any new runners to this spot and make sure they make contact w/ the dirt, or even partially bury them in the humus mix to encourage roots.

As maden the shade said, leave the dead grass. At this point, esthetics don't count! I would put down a nice 1" to 2" layer of Dillo Dirt, and start putting the St. Augustine runners into the DD.
The fertilizer will eventually flush out or disperse and the St. Augustine will recover and your dead strips will disappear. We all learn from our mistakes. Don't ask me about the big round spot in the middle of the front lawn.

And water deeply when needed. That's 1 inch of water which equates to 600 gallons of water per 1000 sqft. It is usually every 7 to 10 days during the summer. Slow soaking type works best to slowly saturate the ground deeply. I usually wait as long as possible before my grass starts to wilt. It is very obvious when that happens. Mowing 3-4 inches tall helps a lot to conserve water by shading the ground and promoting deeper root system.

Congrats! That stuff is hard to kill! It took me about 2 years to get rid of the stuff in my yard. I hate grass. The stuff tries to sneak over from my neighbors house. It's as bad as dollar weed.
TallyHO!

We've learned if you leave the clippings and add organic content and microbes to the grass, nitrogen isn't needed. It just washes away into the lakes and streams, anyway, after burning up the grass.

Here is a link that might be useful: Turf-Lawn Fertilizer Regime

diggerjones,

That's not really the case with organic fertilizer. Basically feeding soil microbes in the soil which is far more cost effective than applying compost. If it rains too much, too bad. That's just part of life.

Beachplant,

I take it that you've never had bermuda grass? Way worse than st augustine...

There's some nice brown yards around here...people tired of watering in this drought and heat, I guess. I don't bother with turf grass in my yard. But too many plants have died. The last part of the summer is usually the worst, plants that survived before start going downhill.

Linda-

I've yet to meet anyone who knows how to water properly around here. They are often surprised just how much is really required. To keep things in perspective...

My little sprinkler puts out 5 gallons per minute. Covers maybe 20 ft by 20 ft so 400sqft. 1 inch needed to thoroughly saturate ground 6 inches deep. That's 600 gallons of water per 1000 sqft for one inch of water. My sprinkler puts out 300 gallons per hour per 400 sqft. My total yard is probably 6000 sqft. You can see how long it really takes to thoroughly saturate the ground to keep everything alive. Most folks do not simply water deeply enough. They never reached the roots... Yet some neighbors don't believe me and water 15-30 minutes 3 times a week while I water every 7 to 10 days or more depending on weather.

Trees are too valuable. The mature trees will have roots covering much further out beyond branches. Water deeply and they will be healthy. Grass happened to get it anyway and stay alive anyway. That's why my lawn looks great without having to water all the time. I care more about trees actually. I have probably 12 trees and still planting new trees till I run out of space. I prefer shade so I'm willing to spend a few more dollars on water bill than paying thousands of dollars to remove trees...