I don't know if this family could be connected.
I have a William Patton of Culmore who died in 1842. The mother of William's natural children was a Nancy/Ann Moore. Culmore is in the Parish of Tamlaghtfinlagan and the Pattons had connections with Ballykelly Pres Church.
His will makes provision for his natural children and Nancy Moore but a codicil was added 19th May 1842. He leaves £50 stg to Gracy Gilloway, £100 to her mother Bridget Gilloway, £5 to Mary McGonigle, £5 to Catherine McGonigle, £5 to Elizabeth Gilloway, £5 to Rachel (no surname) Ballymacran. These may be illegitimate children.
William Patton had a daughter Mary, who died 2nd April 1861. In her will she mentions her five half sisters namely Ellen wife of James Doherty; Peggy wife of Thomas McVey; Betty (Elizabeth Gilloway?) wife of Edward McDevitt, Kitty (Catherine McGonigle?), wife of the late Edward Deehan and Grace (Grace Gilloway?) the wife of Philip Monaghan. If you could find these marriages you might possibly find a connection with the Gilloways of Tullyhoe.
Hope this may be of help.