The fastest way to get rid of St Aug is to never water it and mow it as low as possible. Your mowing height looks good. You have considerable shade, but not too much for St Aug. It will be much more dense in full sun, but it will survive in that.

The second fastest way to get rid of it is to get a fungal disease started. When you get a disease then adding more sod just contributes to the amount of dead grass you have. The only way I've been successful getting rid of disease in my St Aug was to use corn meal at 20 pounds per 1,000 square feet. Corn meal, as it decomposes, attracts a predatory fungus that feeds on the disease fungus. It takes 3 weeks to see improvement and another 3 to see recovery. Corn meal is also an organic fertilizer, so it's not going to hurt anything if you want to put some of that down. A close up of any St Augustine you have left might be enlightening. Close up means 3 inches away.

Most people water improperly. Watering should be deep and infrequent. Deep means 1 inch all at one time. Infrequent means no more than once a week in the hottest heat of summer. With temps in the 80s you can back off to once every 2 weeks. With temps in the 70s no more than once every 3 weeks. The rest of the year you can water once a month. Watering like this should make it very hard for a fungus disease to get started. It should also minimize weed pressure.

Mow at the mower's highest setting. I think you've got this one figured out.

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This is a borderline Limestone Quarry Club soil so we'll treat it appropriately.

Exchange Capacity 20.6: Over-inflated by the excess calcium. I'm going to turn this down to about 10, or a mixed loamy soil.

pH 7.2: Absolutely no barrier to a stunning lawn. I do talk about the ions that set it off down below.

OM 2.4%: In the Fair range. It's fine in a loamy soil, but I wouldn't mind seeing this go up. Always mulch mow, mow all your fall leaves, and that sort of thing.

Sulfur 11: Normal!

Phosphorus 425: My goal in your soil would be about 220. More isn't a problem, but no additional P is required or desired.

Calcium 86.9%: Very high, which is why your pH is also very high. It's not a problem, excess calcium isn't toxic at any level. We just have to live with this, but again, that's not an issue.

Magnesium 6.0%: It looks low, but the high calcium is knocking some Mg out of the soil and inflating the ME numbers to make it look lower. This isn't an issue and we don't need to add any.

Potassium 2.4%: While it looks lower than I like, the same argument applies as for magnesium. None required.

Minor Elements: All in good range, including Boron (amazingly!) I do mention iron below.

Iron 110: It's fine, not deficient, and not a problem, but not going to produce great color at a pH of 7.2. Any time you like, you can feed with Milorganite (or Houstonite in your area) to slowly raise this and very slowly improve the color.

We have been fertilizing with Corn meal and dry molasses for the last 4 years... here is a photo of the grass we do have. It grows in the sunnier part of the yard and is just starting to come out this year. appreciate your input and recommendations.