1930's Adoption

I am looking to see if i can find any of my grandfather's birth family. I have Census records from 1940 showing him as adopted and possibly (if he had a different name) for 1930 showing his parents. His name was Wallace Bitters He was born around 1923-1927- Not even the federal Government could give us his exact birth date He listed his birth parents at John and Francis Dixon The store we were told was that they died in a crash accident around Darlington SC prior to 1940. All of their children were given away and there is no records of it. I understand this is a shot in the dark but i would really love to find information on my blood relatives. Thanks in advance for any help you can provide.