There are three Amyx's who served with the Union in Kentucky.One served in a western regiment (the 37th, under Col. Hanson - one tough officer); another, Caswell, was with Co. A, 47th Kentucky Mounted Infantry, but he died in the service in Aug. of '64 at Nicholasville; the last was James M. who served in the 24th, which did draw men from Morgan County.James M. survived the war and collected a pension for his service, though he was discharged due to an unnamed disability.A James W. joined a Confederate unit, Co. B of the 1st Batt. Mtd. Rifles, from Morgan County.However, the AG's Report notes that he went missing on January 7th, 1862 (perhaps just before Middle Creek?) and "refuses to rejoin."It appears that the Amyx family had some strong service background before Oval parachuted into Normandy.
I'll bet that you are correct in assuming that Tony may have been a relation to Oval as Bethanna and Salyersville are less than fifteen minutes apart.
To add to your information, Ancestry.com lists the parents of Oval Amyx as James Tony and Edna Patton Amyx.I think you are right.