Your best bet is to contact the Attorney General in Nebraska. NE law states:
On August 30, 2009, Nebraska began recognizing CCW permits issued by those states which the Nebraska Attorney General has determined have standards equal to or greater than Nebraska.
So the NE AG Must determine if SC meets NE requirements. Then SC must be contacted and then SC must see if NE meets SC's requirements. I will tell you that SC has one man in SLED who works on reciprocity and he does it part time or I should say when he gets the time. But your AG is where you want to start. Get them to check out SC and then contact them asking for Reciprocity. Then it will be up to SC if they will honor an NE permit/license. For what SC requires to get a permit/license they meet about all other states requirements. It is the other states that don't meet SC's requirements.