Sandy,
If it's any consolation to you, record keeping in Ireland was as bad as early record keeping in Canada.
Being Presbyterian more or less guarantees Scottish origins, Church of Ireland doesn’t guarantee Scottish origins to the same extent but it normally points to he person being an incomer, from England, Wales or Scotland. McDowell is not a native Irish name. Nor is it English or Welsh, and so since it’s obviously Scottish, that’s where the family will have originated.
The broad background is that in the 1600s, some 100,000 Scots settled in Ireland, mostly in Ulster. That represented something like 10% of the Scottish population of the time. In the early part of the 1600s they came as part of the Plantation of Ulster or in the case of Co Down the Hamilton & Montgomery settlement. In the 1640s a 10,000 strong Scottish army came to Carrickfergus under General Robert Munro. It was disbanded in Ireland and many of the soldiers decided to stay on (because land was easy to obtain), and then finally in the 1690s there was a serious famine in Scotland and that led to 50,000 Scots moving across. (It’s only 13 miles away at the closest point. Not a big journey even then).
The outcome of all this migration was that Co. Down in the early 1700s was 80% Scots. There were a few English & Welsh too. But mainly Scots. The area hadn’t been heavily populated by the native Irish and so they were massively outnumbered (and often pushed to one side, in the same way as native Americans were pushed aside by European settlers too). Co Down was basically an extension of Scotland. The settlers brought their Scottish identity with them, as well as a Scottish accent (which is why to this day the accent is significantly different to the rest of Ireland, and why you’ll hear words spoken that would be familiar in Glasgow but unknown in Dublin).
The settlers also brought Presbyterianism with them. Presbyterianism was founded in Scotland by John Knox in the 1500s. The native Irish were Roman Catholic. To this day, Presbyterianism remains the most common denomination in Co Down.
So to summarise, with your family, what you have is someone with a Scottish surname, living in a part of Ireland dominated by Scots and whose religious denomination was an incomers. So without a shadow of a doubt, your family will be of Scottish origins. (As are three quarters of the population of Co Down).
McDowell is a variation of MacDougall. It means dark stranger. (Dubh being black or dark). This link suggests some McDowells may have arrived in Ireland from the Western Isles of Scotland as galloglass (mercenaries) to fight for Irish tribes. If so that’d be in the 1400s and 1500s.
https://www.johngrenham.com/findasurname.php?surname=McDowell
Once the Scots came to Ireland they didn’t integrate with the native Irish. Of course there were some intermarriages, and some early Scots would have spoken gaelic which is just a slightly different dialect of Irish. (The Irish took gaelic to Scotland in the first place, when they invaded around 500 AD under Fergus Mor). But the Scots mostly kept themselves to themselves in Ireland. Intermarried and stuck to their Scottish traditions. The first Robert Burns club outside Scotland was established in Belfast in the mid 1800s, and you’ll find many a Burns Supper here every January. (Belfast was built by Scots, and in 1770 there were only 300 Roman Catholics in the city. The rest of the population were Scots plus a few English gentry).
So your ancestors didn’t see themselves as Irish, even if they had lived here for several generations. The term they use to describe themselves today is Ulster-Scots (that’s Scotch-Irish in the US and Canada).
The strength of feeling about the Scottish identity is partially why Northern Ireland remains part of the UK today, and is not part of the Republic of Ireland. The majority of the population don’t see themselves as Irish, and instead identify with Britain as a whole and for many, Scotland at a sentimental and cultural level. And they mostly hold British passports, not Irish ones (though they can have both).
There’s Highland Games across Ulster every summer and a lot of connections with Scotland to this day. Have a look at the Ulster Scots Agency website for further information:
http://www.ulsterscotsagency.com
It doesn’t surprise me at all to hear that your grandfather perceived himself as Scotch, because he obviously knew that was where his family originated. His upbringing in Co. Down would have been as Scottish as that in Glasgow or Nova Scotia.
In 1843, the famous Irish patriot, Daniel O’Connell was reminded that the Duke of Wellington (who opposed Irish Home Rule) was born in Ireland and was therefore Irish. He responded: "The poor old Duke! What shall I say of him? To be sure he was born in Ireland, but being born in a stable does not make a man a horse." That apt analogy probably sums up the feeling of many an Ulster Scot.
If you are interested in reading a bit more about your grandfather’s background, I can recommend “Eagles Wings – The journey of the Ulster Scots & Scotch-Irish” by Dr David Hume. It takes you through the history of the move to Ireland and then explains why in the mid 1700s so many of those Scots settlers were dis-satisfied with life in Ireland and moved again to North America or elsewhere.
Incidentally that’s another indicator as to your family’s origins. The majority of settlers in North America, from Ireland in the 1700s were Scots. The native Irish didn’t really start emigrating in big numbers until the 1800s due then to a combination of a population explosion, partial and full famines and some other factors. Regarding the mystery over whether there's amissing generation, JAmes b 1745 could have fathered the child, but he'd surely need to have remarried to a younger woman. (His first wife would have bene too old). Have you looked for a second marriage for him?