The "best example" looks like SA to me. Can you afford to re sod the whole thing with SA?

I am trying to identify what variant of St Augustine. It appears to have smooth leaves which I suppose one can then eliminate Native/Common Texas St Augustine.

I am trying to avoid re sodding as the current turf height would need to be taken down. There are a few shallow areas where I could sod, but generally trying to avoid raising the turf height anymore.

Excellent pictures. Lou Midlothian is the best guy I know to identify St Aug varieties.

I'm an organic guy so I'm going to suggest an organic regimen that will surprise you how well it works. Starting now, apply corn gluten meal (preferably), soy bean meal, or alfalfa pellets every month at least through July. Apply at a rate of at least 20 pounds per 1,000 square feet. That in conjunction with proper watering and mowing and your grass will recover. There is no analogous chemical regimen because you would be over applying chems and ruining the grass and soil. At the end of this I'll post a picture of a zoysia lawn treated with alfalfa pellets a month prior to the photograph.

Proper watering means not watering every day or even skipping every other day. Proper watering means once a month now and working your way up to once every 7 days in the summer.

Reset your mower from the lowest setting to the highest setting and weld it in place. There is NEVER any reason to mow St Augustine at a height lower than the highest setting. Once you do that, it will start to look amazing. It will take several weeks or even months for it all to grow up to that height, so have patience. St Augustine will look great when mowed at 4, 6, or 8 inches high. Regular mowers only go to 4 inches. I'm thinking of putting monster wheels on my mower to go to 6 inches (my will will kill me!).

Your photos are great. Don't know what the grassy weed is. Tall St Aug usually will choke out all the other grasses.

Rake up your oak tree trash. The leaves and acorns will not help the St Aug spread. It will keep the soil and grass too moist and allow brown patch disease to come in. Rake it up and pack it into your new compost pile.

Watch that oxalis weed. You have one in one of your pictures. It has a small shamrock leaf. It will shade out St Augustine if it gets hold. Get it all. You can easily do it by hand but you have to keep after all the new seedlings every week for a month.

Here's the organic fertilizer pic. Thanks to mrmumbles.

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This is what really really REALLY tall St Augustine looks like. The grass is growing wild in the sand dunes at Port Aransas. It has never been fertilized or watered. Even the mowed grass has never been fertilized or watered. It is the dog walk area for a condo. The wild grass is too dense for animals to move through it.

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Looks like SA to me as well. What I need help with is what is a good shade grass to grow in North Texas?

Here is a link that might be useful: Texas Gardening Forum