Don't know if it is any help, but I looked the Daymude name up in the books I have from Knox Co. Might give some ideas about Williams parentage and some puzzle pieces. John and Lenora could hve been siblings of your William ?They appear to have stayed there till death so obits from the newspaper or death certificates might give a clue as to parentage, which then might link into you Wm.Also, look them up on the 1910 or 1920 and see what is says about where they were born and where their parents were born.
The name is not common so a check on the availability of will and probate records back inthe right era for Williams father might yield a parent, then go for the census.
Obits and death notices in the Mt Vernon Newspapers: Daymude, William died 22 Aug 1861age 30 yearsson of Abraham wifes name Flora J. Henwood.
Cemetery Records of Knox Co. Ohio Vol I: Old Jelloway or Drake Cemetery Daymude, Alice A.1859 - 1920 Daymude, William H. 1831 - 1861 Daymude, Flora J. (Henwood) 1832 - 1901