I'm afraid you are dealing with the fungus called brown patch. I have heard that if the temp. and humidity add up to 150 or above, it is breeding for fungus. Night temps. of over 70 especially with dew or water on the leaves is prime brown patch time. You may have noticed "spiderwebs" in the morning - that sometimes is associated with the brown patch.

If you have the money to spend, use Heritage (by Syngenta). Yes, it's very expensive, but it should do well. Repeat applications (hopefully at lower rates) may be necessary. Good news is it didn't look very severe at all and even though your grass may look partially dead, it likely is still very alive. Honestly it didn't look terrible to me. There are other less expensive fungicides out there.

20 min. per zone is relative to your system. You should try to get the soil wet 6-8 inches down. 2 times a week should be good. It's your call on the time, just as long as it is thorough. Water early in the morning - just as or before the sun comes up so water will be on the blades for the shortest amount of time.

All the best!

Bottom line is, if it is Brown Patch, the grass is stressed, and that is why it is susceptible to it. Since it is a cool season grass it is entirely possible that it is simply the heat stressing it, but it also would make sense that the soil PH is off - therefore stressing the grass more. I would test your soil again before adding amendments to it.

Maybe someone else here will have some tips for you as well.

Read the label on your fungicide carefully. Look at the temperatures it can be applied at. The problem with chemical fungicides in the deep south is the temperature is never cool enough to use them.

About 2 weeks after you see some improvement in the grass, you might consider applying compost at 1 cubic yard per 1,000 square feet. That will replenish the beneficial fungi which were knocked out by the fungicide.