I think I have some papers that might interest you. I am the 2nd great-granddaughter of Elijah Cumbie Anderson. His youngest son by Elizabeth Sansom, Crowell Anderson, was my great-grandfather. His youngest son, Lucien Anderson, was also very interested in genealogy and through his efforts he contacted various distant cousins and I have a copy of a paper called: THE ANDERSON - BRACK - DOTY FAMILY OF ONSLOW COUNTY, NC, RICHMOND COUNTY, GA, JEFFERSON CO., GA AND MONTGOMERY COUNTY, AL.
This text tells of how Lavinia Brack Anderson, her son Elisha, and his son, Elijah Cumbie all came to Alabama in the 1820's. There are also some abstracts from wills dating back to Elmore Anderson in 1772.
I don't blame you for getting confused about Elijah Anderson. It seems that it was a very popular name in our branch of the family. Not to mention there is more than one Elisha Anderson too.
I will be happy to share the information I have with you.