Marjorie has clarified to me: "Loughgilly" is the civil parish in County Armagh, "Donaghmore" is the civil parish in County Down, Ballydogherty is the townland in County Down where Andrew and Sarah Harshaw lived, from which Sarah and 3 of her sons emigrated.
I also ran across this writeup: not about the church where the Harshaws worshipped, which was Tyrone's Ditches, but nearby church which split.
"The same evangelized truth continued to be taught and the worshipping
community peaceful and prosperous under the ministry of Mr. Turrittine
for 12 years, when an event occurred which suddenly and unexpectedly
proved the occasion of dividing the congregation into two equal parts.
This event was the rebuilding of their meeting house consisting of four
large aisles, but now falling into decay. One party to suit their local
convenience would have the new house built at the village of
Mountnorris about three fourths of a mile distant. The other party from
the same motive would have it erected on the old ground and both
actually began to build in the two places at the same time. Their
common minister, as may be well imagined, was greatly disappointed. For
some time he preached at a bleach mill midway between the two houses
which were being erected for him, and performed the other duties of his
office alike to both sides. Matters were carried on in this manner for
some time until the Presbytery visited the congregation and decided that
the house erected in the village of Mountnorris should in future be Mr.
Turrittine’s place of labour. This decision, which was no doubt
considered partial, rash, and inconsiderate by many at the time,
immediately led the party at Tullyallen to resolve to apply to the
Associate or Secession Presbytery of Monaghan to take them under their
care and supply them regularly with services. This was done and shortly
afterwards in the year 1791 Mr. Wm McAuley was ordained amongst them as
their minister. A few years afterwards a wing of the original
congregation around Kingsmill and remote from both the former places
formed themselves into a separate congregation there and is at the
present time in a flourishing condition."