I'm not a soil scientist like some of the people here, but I do read most of the tests as they come through. I have never seen anything like yours. You appear to have quarry quality limestone suitable for making cement. Be that as it may, I can help with the St Aug even with your soil.

First, be sure you are deep watering on an infrequent basis. I'm in Bandera and have not YET watered my St Augustine this year. We have had almost no appreciable rain, but the dew and humidity have kept the grass dampish. Now that the grass is growing, I suspect it will tell me when to water with some wilting. A problem that many people have with St Aug is watering too frequently.

Always mow at the mower's highest setting. There is never a reason to mow it any lower.

You can fertilize now with any organic (grain type) fertilizer. Get that at a feed store. I like alfalfa pellets (rabbit chow) at 15 to 20 pounds per 1,000 square feet. If you like chemical fertilizers, wait until mid to late May to fertilize. The grass awakens with plenty of energy to make it until May.

Any time now you can spray it for weeds with an herbicide with atrazine. Here is one such herbicide available at most places...

Most of the atrazine herbicides have some purple packaging, but there are some purple packed herbicides that don't have atrazine, so read the labeling. Read the directions on this stuff several times. When I use it I walk backwards with the wind at my back. I try to do it on a calm day, but Bandera doesn't have many of those. And watch the overspray. This stuff takes a few weeks to kill everything, but all that will be left will be St Augustine. Use this stuff once now and try not to use it again this year. If you have to use it again, wait until September after the summer heat breaks.

Since you are new to Austin, you should visit John Dromgoole's nursery.

And looking back at your soil test, I think it's safe to say you can get some potassium sulfate (aka sulfate of potash) and start using that at at least the bag rate. The soil needs potassium, and the sulfate will get neutralized by the excessive calcium. It also needs magnesium, so there is a product called Sul-Po-Mag that has all the stuff you need.

That's great, thank you!