Probably the best advice I can give is that you go to the South forum (the regional one for which the Carolinas is a subforum).
From there, look up the thread(it's usually on the first page) titled "What do you wish you had never planted?"

In that thread you'll read about some of the worst thugs in the plant world. My contribution was oenothera (sundrops). The stuff creates an actual mat of roots that not only hold the soil but are so dense that nothing can grow through them. For me, they were the flowering version of my nemesis..wild bermuda grass.
Mountain laurel and pieris should love the well drained location but their flowering period is rather brief.

It's baked in the summer

Sounds like it needs full sun plants. Daylilies are extremely hardy and you can often get divisions from friends or cheap plants on ebay.

Good temporary erosion control might be to plant pine seedlings (like loblolly). Pines are super easy to get rid of once you move onto your next phase (just cut them down, they don't resprout).

perhaps periwinkle. It's pretty good at helping with erosion once it's well rooted in, and it can handle full sun and full shade, as well as cold and heat. Maybe daylilies and grasses (which also can help with erosion a lot) with periwinkle between? It's really unfortunate that it was scraped like that to begin with.

Catrionna,
My property is exactly like yours!
I feel like I live in AZ, and I don't.
All the good soil is under the house!
I have quite a large hill that is steep also.
Full sun all day on most of it, terrible erosion during bad storms last year.
I bought cheap ROCKS.
Thank god for rocks and shredded mulch.
Not regular mulch, no, shredded mulch.
I still need more rocks, but I have to buy a litle at a time, it's too hot right now.
Besides the mulch and rocks, I planted various kinds of ornamental grass, daylillies, sedum, ice plant, wintergreen little evergreen bush, (can't remember name now), yucca, (who loves the hill), librobe, ajuga, creeping jenny, and spirea, St. John's wort, vinca vine, (hates the sun, but still alive),
and it worked!
The erosion finally stopped.
If you really don't care about having a garden there, Blue rug junipers are also a good choice, evergreen, but you have to mulch good and remember to water so they don't dry out. I have some of them too.
Whatever you do, plant something.
GOod Luck to you!

Thanks everyone for the suggestions, I appreciate it!

I have seriously considered planting invasive plants but could never quite bring myself to do it. The 'what do you wish you had never planted' thread was great! It gave me some good ideas for pretty flowers that tend to behave in my area.

The same with daylillies, periwinkle, rocks, etc. Duh... why didn't I think of that? I look at the nightmare and think 'there's no hope'. Now I have a few ideas and plant names to work with so I can view the mess with a little more optimism :)

It truly is unfortunate it was scraped.

I too have property on a slope. For some of it I have retaining walls and some of it I have not.
Do didn't mention if you are on the morning or afternoon side of the mountain. But it sounds like you get quite a bit of sun, so I am guessing the morning side.
I suggest one of the euonymus varities like e. fortunei (Wintercreeper). This one will keep the soil in place and I like that the leaves change color in the fall and winter. It doesn't matter how much snow falls, it just keeps on plugging. It also survived the recent drought just fine. On other areas I have daylillies. My creeping thyme has only crept slowly, so it must be related to yours! The other thing I find that works well is bee balm. That is because it spreads like crazy where I am. I would love to hear what you find works for you.

How about Rhus aromatica 'Gro-Low'?