What eggplant needs is heat and you should have plenty of that in SC, so I think you'll be fine.
Yes, I'd say Rosa Bianca is the mildest variety I've ever eaten. I've grown it twice. Very good. Another one with the same shape as the Asian varities is Louisiana Long Green. It has mild flavor and from the two plants I had last summer, I'd estimate I picked at least 30 fruits, maybe 40, no kidding. I think the longer, thinner varieties are generally more productive than the bell shaped ones. Usually earlier too, I believe. If you want to use the longer ones for something like eggplant parmesan, you can cut them lengthwise like lasagna noodles and use them that way.
Have fun!
