I've run the William Hocker Long family tree and about 70% of the names on that 1876 plat map show up in it.

Long story short, all the neighbors on the plat map appear to be likely owners in 1864, Jefferson Ray, Thomas G Detheradge are positives for ownership. William Franklin Turner appears to be to be the closest "Turner farm" but is at least a mile from WH Long's farm acroos rough ground and forest which doesn't quite fit. TG Detherage's farm fit's the fight description from the plat. He was Sheriff, Assessor and school teacher. There is a school near his property, its on the other side of the road on the plat map, labeled now as Cherry Grove School. He also was a slave owner on the 1860 slave schedule owning 3. His farm is just off DD south out of Fayette and the "run distance to WH Long's corn field without trees appears to be about 400 yards, of course the whole thing may have happened on the Long farm!

THOMAS G. DEATHERAGE DEAD. Public Administrator of Howard County Overcome by Ajvoplexy. Public Administrator. Fayette. Mo.. April 9. Thomas G. Dentherage, Public Administrator of Howard County, died lust midnight of the effects of a stroke of apoplexy. He was born In Howard County, November II, 1826. taught school many years, and was Representative. Sheriff, Treasuer and Public Administrator of the county at different times. He was a Baptist and a Mason. He leaves a widow, two daughters and two sons. CLIPPED FROM
The St Louis Republic
St. Louis, Missouri
10 Apr 1904, Sun • Page 21

W H Long family tree:
https://www.ancestry.com/family-tree/person/tree/184250606/person/262403562522/facts

I've reached out to the current property owner by email FWIW