I found a Halfacre/McKay family that were in TN and then moved to Ohio. Alfred C McKay was born on 07 Jul 1923 in TN and died 28 Aug 2000 OH. William L McKay SR was born 1917 in TN and died 1999 in OH. They could have been brothers. Alfred C McKay is listed with a John & Opha McKay in 1930 census Middlesborough, Bell, Kentucky. Then John & Opha McKay are listed with one child in 1920 in White, Tennessee. William M McKay born about 1918 age was 2y7m at time of 1920 census. That would place him being born in 1917. I haven't looked at the original document to see if the M is a transcription error, but it also could be an error on census taker. Not like those didn't ever happen (ha ha).
I believe that Opha was a nick name. I believe her real name was Orphie Halfacre McKay She was born 30 Jul 1900 TN and died 26 Nov 1937. She is buried in Sam Flatt Cemetery in Jackson County, Tennessee. Now why do I believe this is the same person. Because on the 1930 census there is a "Harris" listed on it with her and John. Relationship to John as head of house is sister-n-law. Well on Orphie's headstone she is buried with Aileen Halfacre Harris Runyan.
I would take these names when you go to Ohio, because mentioning names may help jog memories. Regardless if it is the same line, it could be related line due to location and timing of migration. I have family trees were sisters of one family married brothers on another, and then the same two families had the reversed of brothers marring this sisters. (These trees aren't always easy because then same names pop up over and over again.)
Let me know if you need any other help.