Glad to see someone else is researching this frustrating line! James K. Adams is my gggrandfather.
I found a possible match for Benjamin Adams in the 1860 Russell Co., Alabama census (Crawford P O, p. 990): B. Adams, 37, b. SC Caroline, 23 b. GA male W.H. age 14 b. GA female A. E. age 11 b. GA male M. A. age 9 b. GA female M.J. age 7 or 9 b. GA
Russell Co., AL is very close to Heard county. I'm trying to figure out where in GA all the children were born; I haven't had much luck with the 1840 census, and that's pretty much the extent of my resources.
I would love to correspond; please post if you find anything!