I am currently using Tifgrand under a cedar tree and it is doing just ok. On the immediate north side of the tree the sod did not take and is slowing filling back in from what did survive. I also installed some in a small "nook area" that is also on the north side of a wall. None of the sod took in this area. If you have very deep shade, I have heard that celebration is good. IMO I would stay away from TifGrand if you have heavy shade, it is expensive and you may be frustrated with the results. Are you trying to get a grass that will match and have same growing habits as Bermuda that you have in another area? If not, you can also try seed that is shade tolerant. Most big box stores have it. All depends on what you are wanting if you use seed or sod.

I am sure others will chime in on the tilling, and the response will be no, no, no...do not till. ha

Instead you want to use a lawn roller to smooth the soil before you seed or sod. Tilling will result in a bumpy lawn. You will have to use starter fertilizer if you use seed.

Thanks. I'm not trying to match any other grass. I just want whatever will do the best in the shade. I read that the big box store shade tolerant would not do well in the heat of N Texas. That's why I was looking into the TifGrand and Celebration. I was also advised that sodding would be better because it would take 6-8 weeks to get a walkable lawn with seed and I would probably get a weed problem in the meantime.

No problem. Not sure on the shade grass seed, have no experience with it. Sod will give you an instant lawn for sure. Seed does take some time and you will definitely have to deal with weeds, since you have to water 3-4 times a day to keep the soil moist. I have no experience with celebration either, but if you search on here for celebration, there are some good comments about it.

I seeded a 3/4 acre lawn with Bermuda 2 years ago and still have weeds to deal with in thin areas, and the recent rains has not helped my problem, but I have the patience and have no problem spending hours in my yard to get it where I want it to be.

If the previous owners let the St Aug die, it was from lack of water, not too much shade. If there is too much shade for St Aug, then no bermuda will survive. St Aug must be sodded. If you want it to spread this year, you may be too late, although with the weather prediction I just heard for the rest of the year, this might be a banner year for grass like St Aug.

Do not rototill. Just as was mentioned. And do not bring in any more topsoil. I'm sure your contractor put in exactly the right amount. In fact, never bring in more topsoil unless a low spot develops that must be filled for proper drainage.

You won't need any fertilizer until you have roots to take up the fertilizer. You won't need peat moss because it really doesn't do much of anything anyway.

If you want to do something, you can use organic fertilizer. Organics work to improve the health of the soil biology. It is the healthy soil biology that feeds plants, so using organics will only improve things. The fertility caused by the organics does not wash through like chemical fertilizers do.