Did you have access to "The Achison/Atchison Families" by Nellie Wilkin Cooke (KS 1953)?--I was told there was a public copy in the DAR records, but don't know for sure. A lady who worked in the DAR and did a painstaking job of researching her own Acheson roots said this was one of the more accurate sources (and not as confusing as the 1912 account, though it uses the 1912 manuscript as one of its sources).
If you have not seen it and would be interested I would be glad to help you get a legible copy (it deals mainly with the descendents of the eldest son, Matthew, but touches on other branches of the family as well)
Just let me know---I would be interested in any new information on the family in any case. yours, K.Bain