Your first step has to be to promise to water the lawn at least once a week during the summer. That's why your grass is dead in spots. St Augustine does not go dormant when the drought hits, it goes dead. During the hottest part of summer I water once a week for 1-3 hours per zone. The rest of the year (like now) I try to water every other week. Sometimes the grass will tell me it needs more frequent water. How often you water has to do with your grass height, soil, humidity, and rainfall.
Next adjust your mower to cut at the highest setting. Tall St Augustine does a much better job of getting through droughts.
Fertilize on the federal holidays. I start on Washington's Birthday (3 weeks prior to our last frost date). Then I fertilize again on Memorial Day, 4th of July, Labor Day, and Thanksgiving. I use those dates because they work and they are easy to remember. I like to fertilize with ordinary corn meal and/or alfalfa pellets. When bought at a feed store they are 1/6 the cost of commercial organic fertilizers that have the same ingredients. The rate is 10-20 pounds per 1,000 square feet.
If you want to do something for your soil, apply compost at a rate of 1 cubic yard per 1,000 square feet. Fall is the best time to do that but any time is fine.
If you want to use molasses, I would wait until after the compost is down or the grass has filled back in. If you want to aerate I would wait until fall. Seed is never used in St Augustine.
Watering and mowing (when done as above) are really all you need to do. There is no extra cost or anything you have to do unless something else pops up. The St Aug will be thinner in the shade than out in the sun. If it starts to look dry out in the sun, water it.
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