Hello,
This is a long shot, but I happen to have some information regarding a Rev. John Hart (spelled his own name as "Heart", but the records of the Presbyterian Fasti record it as "Hart"), who came from Hamilton, Scotland to the church at Taughboyne, County Donegal about 1655/66. (this was an area known as "the Laggan"). He ministered there for some 30 years, and died in 1687.
Rev. Hart had a son named Samuel born in Hamilton, Scotland, while he was a minister there (prior to that, Rev. Hart had been a Dunkeld, Dunino, and Crail, Scotland). He was a graduate of St. Andrew's University in 1637, and married in 1644 at Edinburgh, Scotland to Agnes Baxter (or "Backstare"). Rev. John was buried in the churchyard of Taughboyne (also called Monreagh). Agnes was buried in Greyfriar's Kirkyard in 1689, so it appears she returned to Edinburgh, where she probably still had relatives. John and Agnes had a daughter, also called Agnes, who married Rev. Robert Craighead, another Scottish minister who was appointed to the church in Donaghmore. Rev. Craighead married Agnes, daughter of Rev. Hart, and eventually, he became the minister of First Londonderry Presbyterian Church.
Your Harts in Donaghmore were there nearly a century later, and I can't make a connection, but I thought you might be interested in Rev. Hart/Heart.