Atlanta used to be in the transition zone before the Earth started getting warmer. Now I think it is in the northern part of the south - right where Atlantians think they are anyway. With that in mind, you might look at St Augustine. Zoysia really wants more sun than the sellers tell you. All the St Aug varieties will do okay in the shade while some do better than others.

Never rototill in preparation for sod. You can do that for plants in the garden, but not for sod. Why? Because that fluffy soil has to settle. It starts off by settling unevenly and then gets worse as it settles more over the next few years.

How do you start? With St Augustine I would buy a few pieces and put them down in the shade. You can make a nice place for them if you want, but it should be sort of cleared. That piece will take a few months to rest and then in the fall will start sending out runners about 5 to 10 feet in all directions. That will happen again in the spring and fall every year covering up all the other grassy plants including the bermuda. Water it daily until it knits into the ground. Then transition to deep and infrequent watering (1 inch all at one time, no more than once a week). Mow it at the highest setting every other week. Fertilize only the St Augustine and all its runners with organic fertilizer every other month this year and then on Memorial Day, Labor Day, and Thanksgiving in the future. St Aug is a fairly low hassle lawn. The more pieces of sod you start with, the faster it will spread and cover up what you have now.

In order to get the most pertinent advice, you need to show pictures of the overall area (no close-ups. Let us see how the tree canopies relate to the yard. Show broad scenes of slightly overlapping pictures taken from a camera SINGLE point of view (not from different locations, except where you are photographing a different scene.) I lived in Atlanta for a good number of years and had fescue and had no complaints about it. It browned out in the hottest part of summer unless I gave it extra water, but it was very nice looking the greater part of the year.

As trees grown and produce more shade, it is often the case that lawn under them must be done away with and replaced with groundcovers.

Will work on uploading a few photos