You can forget about using corn meal for now. If you already applied a fungicide, then you killed off the predatory fungus which is attracted to the corn meal.

I would give the fungicide 3 full weeks to show improvement. If it does not fully recover or look much improved, then apply some compost at a rate of 1 cubic yard per 1,000 square feet. A week after that you can try the corn meal at 20 pounds per 1,000 square feet. If you cannot find corn meal at a feed store, you can try cracked corn (feed store) or corn flour in 25-pound bags from a Hispanic oriented grocery store. Don't get the flour that has baking power or any other additives.

Your watering is likely the issue. You clearly have been reading this forum to learn about corn meal. You likely have come across the watering regimen (deep and infrequent) that is promoted here and in most lawn forums. Here is the idea behind deep and infrequent watering. When you water deeply there is water deep in the soil for the roots to get. But if you water every other day, the roots don't need to grow any deeper than the surface to get moisture. But if you withhold water for several days/weeks, then the roots will grow deeper in search of moisture. As long as there is moisture deeper in the soil, the grass will not wilt even though the surface is dry as dust. I have a house on the edge of the Texas desert with very tall St Augustine. The height was an experiment to see how long the tall grass could go without watering. I have a few parts of my lawn which have not received anything but rain since October of 2011 when I bought the house. This year we had a few nicely spaced showers which allowed me to extend and not water for months. I finally started watering the entire lawn in mid July. Temps are running right under 100 degrees F and I water the full sun part of the yard once a week. The shady areas I water once every 2 weeks. Again, my shortest grass is 12 inches high, so this is not to say it will work perfectly for my neighbors, but for you with temps in the high 80s to low 90s, deep infrequent watering should be fine. I would be inclined to push for once every 10 days to 2 weeks. But you have to water a full inch at a time. Measure an inch using cat food or tuna cans places around the yard. Put some in the fungus affected area and some in the dry spots.

You might have to wean your grass onto this deep and infrequent plan. Water deep to start and watch for wilting. As soon as any part wilts, water deeply again. Soon enough that time will stretch out until you are watering ever week or so.

Finally you have to adjust for rain. If you get rain, restart your watering calendar. If you get an inch of rain, you should not need to water for a week or two. If you get 1/2 inch of rain, then only water 1/2 inch when you normally would have watered.