Ask Mr. Smarty Plants

Probably offering you our deepest sympathy is not going to suffice, is it? Actually, the word is that when you are trying to rid an area of weeds, rototilling (which you didn't say you did) is not the way to go, because you just pull more seeds and roots to the surface where they can germinate.  But, even if you took it out with a sod cutter, obviously the Digitaria texana (Texas crabgrass) arose again. And it's probably no comfort that this USDA Plant Profile map shows it growing only on the Texas Coast. There is also, of course, Digitaria arenicola (sand crabgrass) (only on southern tip of Texas), Digitaria cognata (fall witchgrass) (widely distributed from Texas east and into eastern Canada, and Digitaria hitchcockii (shortleaf crabgrass), found in the  Big Bend area, South Texas and, you guessed it, Travis County. This is information you don't need and won't help, it is all basically the same, and very difficult to get rid of. 

To be honest, we're stalling because we really don't know the answer to your question. One thing we have realized is that crabgrass is an annual weed, with shallow roots. Starve it of light and water, don't let it go to seed, and it should be gone. Of course, you will always get seeds from other places, but if you are vigilant and pull it out as soon as it appears, that can be minimized. We found a website from One-Stop Tree and Lawn Care with a section on crabgrass that had some good suggestons. From the Home Improvement News and Information Center, read this article Prevent or Eliminate Crabgrass in Your Lawn. From the website All About Lawns, read the 10 Steps to Become Crabgrass Free. 

Finally, since it really is too hot to be planting much in the way of native plants, or anything else for that matter, you might consider this article on Soil Solarization from  Arid-Southwestern Gardening Information. Perhaps an area you are not ready to plant yet, but where lawn was and crabgrass is would be a good candidate for this. 

We agree with you on avoiding the chemicals in your crabgrass warfare. You don't want to risk contaminating your soil nor take the chance of accidental damage to nearby desirable plants. We think continuing to mulch and hopefully shade out the crabgrass, pulling out what does emerge, and never allowing it to go to seed (which it will do all season), although labor-intensive, is the best and most environmentally friendly way to go. 

And to be sure you know your enemy, here are pictures of crabgrass.