Waco is a tough environment. The native soils are normally adaquate. The growing season is long, but summer moisture is an issue, as I am sure you are aware. I come for the Texas gulf coast. Before I answer your questions with questions, I will give some general tips. Don't mow the lawn low. Allow some growth between cuttings, especially if you the lawn is struggling. Eveporation is your nemisis. Give your soil and roots some shade and don't cut too low. Find a grass that works for you. Bermuda and other 'wire grass' species will do well in heat, and survive. It is hard to make a tidy lawn. Crab grass is another that will do well in your heat, but who likes crab grass. St. Augustine may be your best bet, but requires watering. I have not had a lot of experience with buffalo grass or the new zoysia varieties; but worth looking at. I know it is a pain to replant an established lawn. What are you working with currently?
I like to collect all my clippings rather than having a mulching blade 'recycle' the cuttings. I think thatch becomes a problem that adds work to your annual duties. I prefer to have a mulch pile and hot compost until it is well broken down.. Then when things get hot and starts to thin, you can come over an area or the whole yard and top dress. It looks like crap for a few weeks, especially if the mulch has not aged fully. But during the few weeks of killer temps you can cover your plants to seal in moisture; and feed the soil. After the heat spell the grass will pop up through and thrive. You have fed the soil which feeds the grass, and kept the heat from baking the roots. A small price to pay for the effort. The lawn is going to look bad anyway. Make it a 'remodel'. If your neighbors are out long enough to object, they likely have mild heat stroke themselves. Be kind.
I have mixed feelings about compost tea, but it may be something that works for you. Make a batch and water with it when you feel the soil needs a boost. I have come to the belief that the bacteria population will balance itself to the food supply and the tea will give you a few days of boost, and then normalize. Hardly worth the trouble.
With this method you also get great compost for a garden if you have one. I worked my way through a few years of college mowing grass (back when one could.) The customer with the absolute best garden and a certified green thumb, would tell me to bag his yard, but dump the clippings in his gardens randomly. He would let the small piles feed the worms who did all the work for him. I reduced work and input for us both, and his gardens were always in terrific shape.
Always (never say always) water in the early morning. It soaks in, evaporates less, and the 'lens' effect of the water droplets don't hurt the blades. What type of soil are you working with? Clay, loam, hardpan? Take a screwdriver and stick it in the ground. Get a rough idea of how much force it takes to go 6 inches. After 200psi of pressure, roots have a hard time growing and it is indicative of hard packed non-aerated soil. If it does not go in smoothly, aerate. Take a broadfork, insert and lift the soil. Don't turn it over. Just 'fluff' it. If it takes a lot effort, like having to jump on it, Waterlog the lawn and get the tines deep. Fluff throughly as frequently as time allows until the screwdriver goes in 6 inches like a garden soil.
Water, Air, Food. That is all a lawn needs, just in the right amounts and in approxiamately the right time. Find the grass species you like best that will grown and start seeding in the fall (october and november for you.) If you want green grass in the winter/cool months try a winter rye or even grain rye and buckwheat and clover after the summer grasses start to flag in September. They will die off when it gets warm again in march and april and the warm season grasses will take back over. So sometimes you have 2 lawns, one for each season. (for non texans there are only two seasons. Summer and Not Summer.)
One more tip to add... The gardener I mentioned had a 'secret trick' that he loved. Back before glyphosate was sprayed on everything, he would get a load of horse manure. He would let the stall litter age in a pile until it had broken down. Horse manure is way to 'hot' or green to use in your garden or on a lawn until it has age at least year. He would use it fresh. His trick was to add a few scoops to a watering can each time he filled it with water. When something was struggling he would hit it with that nitrogen rich, but dilute water and the plant would respond. now with so many hay farmers using 'roundup' type chemicals, it is a gamble. But if you can find a small batch of horse manure, take a hand full of rye, buckwheat, clover or other small fast germinating seed and water into the pile. If it sprouts and lives for a week, it is likely chemical free and safe to use once the manure has aged. If nothing germinates or dies soon after, haul that toxic waste off your property (and apologize to your plants for trying to poisin them.)
Good luck. WELCOME. and keep us posted on your results. Edit: And you have a lovely yard. You don't need to change a thing.