My favorites are:

Canadian Hemlock
Sassafras
Sugar Maple
Silver Maple
Sumac
Arrowwood Viburnum
Fothergilla
Witch Hazel

Sweetshrub, Calycanthus floridus.
Mapleleaf viburnum, Viburnum acerifolium.

Both of these do well in part shade conditions and can handle dry (they do need some water the first year). It would be best to plant in the fall, of course, that will give you time to get the privet out too (good for you!). I would also suggest taking out the goldenrain tree - it will prevent future seedlings and it should give you more light in the area. More light will allow what you plant to grow faster.

If you haven't been to a Georgia Native Plant Society meeting, I'd encourage you to go to the July 8th one (there's no charge, you don't have to be a member). The topic is:

Jim Rodgers from Nearly Native Nursery will present "Jim's Top 10 Native Trees, Shrubs, Perennials, and Palms".

Nearly Native will be bringing some plants to sell as well.

Here is a link that might be useful: GNPS

I would also consider Native Azaleas - many species and cultivars available in this area.
Also, Oakleaf and 'Annabelle' Hydrangeas
Buckeye (Aesculus sp.) - Bottlebrush, Yellow, Red or Painted
Hearts-a-burstin' (Euonymus americana)
American Beautyberry (Callicarpa americana)
Chokeberry - Aronia (Photinia)- Red, Black or Purple
Spicebush (Lindera benzoin)
Hollies (Ilex sp.) Winterberry, Gallberry, Inkberry or Possumhaw. (M/F required). Small plants are usually unsexed seedlings. I once purchased 6, all were male!
Winterberry is a popular garden plant and many cultivars have been selected and named. Sex has been predetermined and is so indicated.
Some of these shrubs are rated Facultative wetlands, but can be found (and grown) in fairly dry uplands (my garden, of late!)
Supplemental watering may be necessary during establishment of any plants these days. Should be monitored for the first couple of years. Late fall or early winter is best time to plant deciduous shrubs. A thick layer of mulch around the plant (leave a few inches clear of the trunk/stem for air circulation) will prevent rapid moisture evaporation. Covering an area about four times as large as the root system prevents dry adjacent soil from "wicking" moisture away from the roots.
Rb