RR,
I am not sure if this well help you or not, but in the northeastern/central Louisiana parish of Catahoula, there is a small community named Peck. I have often wondered where the origin of the name began. You stated that the family had substantial land holdings in Louisiana, so that may be an avenue to pursue, as this community is largely a cotton-producing one of the state. Let me know if I can help you further.
Terry