I agree with @Dave E. and @Genny Li definitely do not pay to have your HVAC ducts relocated to the attic. In the summertime in South Carolina your outside humidity will be high. If you put a humidistat in your crawl space in August and measured the humidity levels they could easily be over 90%. This is what is causing the moisture damage and mold. Best solution is to encapsulate and insulate (the walls) of the crawl space. Then either use a dehumidifier especially for crawl spaces or dump some conditioned air from the ducts into the crawl space. This will dry out your crawl space. We had the same issue here in Tennessee and my humidity levels were at 99% in the summer before encapsulating the crawl space and dumping some conditioned air into the crawl space. Now it never exceeds 50%. One word of caution is to check the radon levels after encapsulation to make sure they are in an acceptable level.
If you want to get into the weeds of crawl spaces and their problems here is a good article:
https://www.greenbuildingadvisor.com/article/new-vented-crawl-spaces-should-be-illegal