A possible clue, though I don't know how to exploit it.
He was buried in the Friends Burial Ground at Moylena, though he wasn't a Quaker (he was a prominent Methodist). The sign over the gate at the burial ground reads: 1701: Moylinny Quaker's Cemetery, Burial Place to the Reford Family. The Reford family had been Quakers, but I'm told that by the late 1700s to early 1800s they were Presbyterian. Why was John McDowell entitled to burial there? A possible answer is that he had a Reford ancestor. Was his mother a Reford?
Unfortunately a McDowell-Reford marriage at a date that might fit John's parents, and a baptism for him, would fall in one of the gaps that PRONI notes in the records of Antrim First Presbyterian (Millrow).