That's a tough combination: native, evergreen, under 30 inches AND fast-growing. Not sure you can have all those characteristics (and be able to locate some of it).

A classic ground cover is Rhus aromatica 'Grow Low', but it is not evergreen. Leucothoe axillaris is evergreen but not necessarily fast (not the first two years) and is more than 30 inches tall.

Phlox subulata is native, evergreen and low growing - readily available in stores all over the place right now because it is blooming. Don't know how fast it is.

You could certainly consider a mix of things. Shrubs and trees usually provide the best root system to hold a slope, so a few of those strategically placed with some groundcovers for looks might be a good approach.

Here is a link that might be useful: Georgia Native Plant Society

I don't know if wintergreen would fit the bill? What do you think, Esh? I don't know that it would stop errosion. It doesn't move very quickly, that's for sure.

Dwarf itea is great for holding in slopes, but it's not evergreen.

By "wintergreen", do you mean Chimaphila maculata or Gaultheria procumbens? Chimaphila would not be suitable and I don't have any experience with Gaultheria - it is only native to the far northern counties of Georgia. Just a little bit of research says it does not like heat and humidity and prefers "cool summers".

Last year I planted at least a dozen varieties of plants/bushes on my slope. I ventured outside and I see that butterfly bush (I think) has done well. I can see some mexican lavendar but mostly I don't see other bushes I planted.
:(