you still can use pre-em. Lesco 0-0-7 from Home depot will still control some weeds.

If you want a decent looking st augustine lawn...

You must mow them at 4 inches height. They do much better in shady area at that height. You must fertilize to thicken them up. You must water deeply and infrequently. Since you have pecan tree, I would say 2 inches worth of water every 2 weeks. That's 1200 gallons of water per 1000 sqft. It must be slow soaking type so the ground can absorb all the water without water running off. That will saturate 12 inches of soil where all the roots are.

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What it looked like before...

Anyway, if you water all the time like 3 times a week for only a few minutes, you will promote a ton of weed growth but not grass or trees. They have shallow root system so they like frequent watering. The weed seeds need frequent watering to germinate and grow. When you mow high, it prevent sunlight to the ground for weed seeds to germinate as well. Tall grasses in shade will absorb more sunlight and perform better. Also it promote deeper root system so it cuts down frequent of watering. I've seen my st augustine grow 16 inches of roots... I usually water every 2 weeks. I tend to get lazy at times with manual watering but they turn out fine. It proves that st augustine is not water consuming as everybody claimed to be. I just don't think they have proper knowledge on how to maintain st augustine the right way. Actually, bermuda and st augustine require same amount of water to look good. In my opinion, it's a lot easier to garden with st augustine and maintain st augustine than bermuda ...

I use organic fertilizer like soybean meal from feed store. No weed control of any kind. I water deeply every 2 weeks.

The weeds you mention must be pulled (or sprayed). They will invade St Aug and shade it out. Henbit is easy to pull. Oxalis comes out easily enough with moist soil. You can collect a lot of it and pull out a central root. I have not tried to pull the others. If you take these out by pulling, just keep after it when they try to return and you'll get them.

Wild violets are very hard to beat. Pulling them easily snaps a taproot/rhizome system, and can actually divide them into multiple plants. They tend to be occur in patches, but they also spread by seeds. In the North, we have been pretty successful with Triclopyr herbicides, but you shouldn't use Triclopyr on St Augustine. People say that 2,4-D and Dicamba works if you apply multiple treatments, but before we had Triclopyr I gave up with 2,4-D/Dicamba after 5 treatments only stunted them. Maybe one of the Deep South folks knows how to beat them. All I can pass along is "don't pull them" unless you can keep it up until the roots run out of stored food.

Wow, Lou, your St Aug looks fantastic! Lush green grass always puts a smile on my face.