Forgive the long time I have taken to answering this... haven't been on Ancestry in a while. I was aware of your third great grandfather Aaron and his marriage to Mary Zeagler, but did not know anything of his descendents so would love to share more information with you. I have a lot of info back to John Adam and Mary Ann Jackson.
The Alice on the 1870 census was John Adam's daughter Alice Adelade, whose age was 20, not 70. Handwriting on census must have been hard to read. According to my information, she married Edward Atkinson of Clearmont, Sumter County, SC in 1875. (this was from family information, not anything I have documented.) Please email me at mcox1263@sc.rr.com so that we have fill each other in on our respective branches of the family.
Margaret Shirer Cox