I'm a bit, well very, puzzled actually about this bit-
The Hunters I've traced were in Mullans townland, Clogher parish, County Tyrone. "Henry Hunter" (sometimes called Harry) was counted there in various records, but Jon says he's researching a Henry Hunter from Ballyclog, just outside Stewartstown, so these are different men of the same name. Jon has found evidence suggesting his branch of the Hunter family came from Aghadowey Parish in Co. Londonderry.
Aghadowey Parish is quite a distance from Ballygawley in County Tyrone. There is also a Ballygawley townland in Aghadowey Parish. I've been tracing the Aghadowey/Agivey Hunters for over 30 years can trace them back to Scotland in 1600s but have never come across any connection with Hunters in Tyrone.