The Acheson you are seeking was NOT from the Acheson line descended from Mathew, Humphrey, David, & John.Members of the line above first settled in the Counties of Washington, Louisa, and Muscatine, all near Keokuk, IA.
I have looked for a connection before to the Keokuk mayor, but it is not there.An Acheson was one of the first mayors of Keokuk. The area now known as Keokuk County was used by the Mormons as a river crossing and staging area for further westward migration.The importance of this area increased as the Mormons grew crops to supply emigrant wagon trains headed West.Your answer will probably be found in the history of Keokuk, or at the Mormon church.
There was a George Acheson, descended from the Alexander W. Acheson line, that lived in Jefferson County, immediately Northwest of Keokuk County.He was one of the first lawyers in Iowa, having arrived from Pennsylvania in 1843 and forming the partnership of Slagle and Acheson of Fairfield.
I hope that this information will help you sort out the numerous Achesons in this area.Good Luck!