I think the only problem in your question will be that most
movers will not let you ship guns through them.
My suggestion is unload them all and pack them in your trunk and come on down. Once you hit the S.C. boarder.... load one of the handguns and put it in your glove box or closed in a center console.
Unless you already own property in S.C. then you could already have a CWP from here and could carry.