There is a Joe H. Adkison b. 1874-d.1935 (married an Emma Unknown, she was b.1876 d.1952) who is also a son of Duncan & Sallie.
He has a brother named Perry (b.1887 d.1981, son of Duncan & Sallie)who married a Winnie Unknown(b.1888-d.1977).I don't think Perry & Winnie are Elzie Carl Adkison's parents.Perry & Winnie had two children, both female, Elsie Lee & Dorotha Ann b.1916 d.2001(I have Dorotha Ann's obituary, my in-laws knew her, she lived her later years in Houston).Dorotha also has a son named Perry, b.1938 d.1988.
With this in mind, IF you are a desendent of Duncan, possibly Joe & Emma are Elzie Carl's parents??Do you know anything about Elzie Carl's siblings?I will check my sources also.
Children of Duncan Adkison & Sarah"Sallie" Beasley: 1) Mason Adkison b.1869-d.1951 m.Lou Cindy Bradshaw 2) Jessie Mannel Adkison b.1870 d.1901 m.Francis Ellen Bradshaw (I have a lot of info on this family) 3) Frank Adkison b.1872 m.Edna Nora Hayes 4) Joe H. Adkison b.1874 d. 1935 m.Emma b.1876 d.1952 5) Sam Adkison b. 1878 m.Anna Bradshaw 6) Leona Adkison b.1880 7) Alice Adkison b.1886 8) Perry Robert Adkison b.1887 d.1981 m.Winnie b.1888 d.1977
I have a lot of info on Mason, Jessie Mannel, Sam & Perry Robert all sons of Duncan.
Let me know if the Joe & Emma route checks out.If not, I have another possibility for you to consider.