Have you seen the will for George Cagle dated 30 Nov 1868 in Stanly Co. Will Book II? In this he mentions his Ilegitimate son, Ely Huneycutt and wills him "one hundred fifty acres of land where I now live, by his mentaining my daughter Beedy M. CAGLE during her natural life, in case she does not marry, and if she marrys he shall be released from that obligation by his paying her one hundred dollars"
In the 1870 census, the family you mentioned headed by Frances Huneycutt, was living next door to this George Cagle.
I also believe this is why Eli F. Cagle is listed the way he is in the marriage records. He was ilegitimate and his father was George Cagle and his mother, Manisa Huneycutt.
I also found a marriage to a Maniza Huneycutt to Gabriel Barbee 26 Oct 1860 by G. D. Whitley, JP Book I page 37, but couldn't find a marriage for her under the name "Barbee".
Have no idea if this is the same Maniza or not, but think it is possible.