You got what I had before I discovered corn meal. Corn meal finally got me over the hump and the grass is absolutely normal in that spot now. You can put down new sod every week, but it's going to die. You have to get rid of the disease. Once that happens, you will not need to redo it with new sod. The sod that's there will come in fine.

Your soil pH is perfect for St Augustine. Don't waste your money trying to fix it. What that indicates is your soil is made of calcium sand instead of silica sand. You can pour straight sulfuric acid on it from now on and all you'll get is a deeper hole where the sand dissolves. Much of Texas soil is 8+ and St Aug absolutely thrives.

Your problem is water retention...if you call that a problem. Actually your problem is you continue to water despite your water retentive soil. Clearly your initial watering routine is going to have to be different from the "normal" 3x per day routine. If your roots are knit into the underlying soil, back off on watering. Watch the grass for signs of wilting. When it wilts, then water and start watching it again. This time of year I would be looking at watering once every 3-4 WEEKS.

If it has been at least 3 weeks since you used a fungicide, then you might want to try corn meal along with a light dusting of finished compost. A light dusting of compost means 1/2 to 1 cubic yard per 1,000 square feet - or even less. The reason corn meal works against disease is that as the corn decomposes on the soil, a beneficial (predatory) fungus appears on the corn. That predatory fungus will destroy the disease fungus. The trick is that you have to have at least some of the predatory fungus in your soil to begin with. By applying a chemical fungicide, you usually kill off the beneficial fungi leaving none behind to keep the disease out. Compost will reintroduce the beneficial fungi to the soil which will then populate on the decomposing corn. Corn takes 3 full weeks to show any improvement. The improvement will be that the new grass will grow to full height without getting any spots or lesions on the blades. You can see the spots in your second picture of the second post near the top of the image. St Aug should have no spots whatsoever. Here are some pictures. The first is normal and the second shows the fungal disease spots.

As I recall these two pictures were of the same area taken about 6 weeks apart before and after (or after and before) corn meal treatment.

Okay so generally here's how you care for St Augustine.

Water. Deeply and infrequently. Deep means 1 inch all at one time. Infrequently means once per week with temps above 90, once every 2 weeks with temps in the 80s, once every 3 weeks with temps in the 70s, and once every month the rest of the year. In your case you might be able to stretch these frequencies out some.

Mowing. Mulch mow at your mower's highest setting every week or two. In the spring when it's growing very fast, you might need to mow 2x per week. Tall St Aug is much healthier and needs less water and fertilizer than short mowed grass. St Aug can be extremely healthy at 32 inches tall (I have pictures), so letting it get up to 5 or 6 inches is not a problem.

Fertilizer. Once on Memorial day, once on Labor Day, and once around Thanksgiving. Seeing as how you're so far south you might move these to once in early May, once in late Sept, and once around Christmas.