Green ash (Fraxinus pennsylvanica) is native to this area (I have it in my own yard naturally). Several locust are also native: Robinia hispida (bristly locust) and Robinia pseudoacacia (black locust). I see the white flowers of black locust on roadsides when they are blooming - looks like white wisteria.

My parents have a Lady Banks that I gave my Mom over 30 years ago. It grew into a huge bush without any care at all.

Everything I have read about the Lady Banks seems perfect for here as far as the heat,etc.; but what about the heavy red clay? Honey Locust or even Purple Robe, are my favorite two locust, that I have grown in other climates. They will grow in harsh conditions, they are brittle, subject to wind damage, but I love them. I just want to be able to plant some things that will survive in the native heavy clay soil, without the trial and error. I have moved and planted my sweet woodruff by my front door at my last three homes, that's one thing that will give me a sense of home, in a new yard.

I just want to be able to plant some things that will survive in the native heavy clay soil, without the trial and error.

You might want to consider native plants - they are perfectly adapted and there are many beautiful ones to choose from.

Here is a link that might be useful: Landscaping - plants of the Georgia Piedmont

Lady Banks will do great. Just dig a good hole where you want to plant it and add some peat moss or something. You don't have to dig up a whole bed or anything, just its own hole. Another bonus with them is they are thornless and evergreen. I have one now that has survived total shade, but I need to move it because it does not bloom.
I have always wanted some Sweet Woodruff, so you have resparked my interest in getting some.