Dewhitewolf is right...
non resident Fl permit is not recognized in S.C. The only way to get a non resident S.C. permit is to actually own property in S.C.
With all that said... go for the Fl permit... it will give you a lot of states... and yes you should be able to get one of those... takes some time and effort but is well worth it.
You know that if NY would recognize other states permits then you would be good to go with one of those, including S.C.