John, I'm a Womack descendant and have ADAMS in my files who are members of your family, though not my direct ancestors. Katherine (Catherine) Elizabeth Adams married William Green Womack about 1839 (probably in Butler County, whose courthouse burned 1853). They were counted in the 1840 Butler County, Alabama, census with one male age 20-30, 1 female age 15-20, 1 female under age 5.
In 1845 William Green Womack was killed by a slave (have graphic family stories), leaving widow Katherine and children Martha Elizabeth (b. 1840, married John Hobdy Adams and moved to Polk Co., Texas), Leonora (b. about 1843-1844, married James P. Straughan, lived Polk Co., Texas) and William Francis (b. 1845? not traced further). I have lots more on descendants if you or other Adams cousins are interested.
John Hobdy Adams (CSA, Texas - see Polk Co. website) was son of Samuel Goode Brook Adams of Macon Co. -- a relative perhaps of your William E. Adams?