I've done similar things in the past, and I called the NC and SC state police to ask them how they'd prefer I handled it. They told me that unloaded, locked in a case, ammo separate was ideal, and would not get a traffic cop riled up, should I be stopped.
If you're just making the trip in one shot, you're good to go; you're allowed to go from point A in a state where your gun is legal, to point B, in a different state where your gun is legal, without restriction, even if that trip involves going through a state where your gun is *not* legal. You're not allowed to stop for any length of time in the draconian state, but short stops for gas and to use the catbox likely won't cause problems.
Now, I seem to recall that SC has a bizarre law on the books that said that, unless you had a CCW, you could not carry a loaded gun in your vehicle. Ever. Unless you kept it in your glovebox. [whacko] Then you could do it without a license or permit... I just don't see the point of such a law. (Don't take my word on this, BTW; I lived in SC 5 years ago, and my memory is fuzzy).
-BP