I scan all the posts about early-days Carolina Alexanders and noted your mention of Joseph Lowery Alexander. Is he the Joseph Lowery who lived in Burke County in the area now known as Dysartville? If so, I would like to get you to do a brain dump on Joseph Lowery's family.
From circumstantial evidence, I believe that Joseph Lowery Alexander was my wife's gggg- grandfather. Her ancestress's name was Nancy Alexander, born about 1796; she and her husband Samuel Dysart lived by a Joseph Alexander in 1820, and, after naming their oldest son for Samuel's father, they named their second son Joseph Lowery Dysart.