You say that Eliza’s gravestone gives her place of birth as Kilbride. Unfortunately there are over 30 townlands and parishes in Ireland called Kilbride so the problem we face is trying to identify the right one. If you can provide her parents names and her approximate year of birth we can search to see if there is a record of her baptism. You haven’t given any dates but if her husband died in the civil war then I’m guessing they were both born pre 1840. If so, not every parish has records for that period so it can be tricky.
You query the comment someone made about how the family reportedly treated Catholics and did not see themselves as Irish even after being there over 200 years. I can probably offer a suggestion as to what that might be about. What denomination was the Kinch family? Were they Protestant? Looking at the 1901 census of Ireland there are 200 people named Kinch. Three quarters were Church of Ireland (Episcopalian) with only about 50 Roman Catholics. Statistically therefore, your family seem more likely to have been Protestant than Catholic. If Church of Ireland, then they may well be descended from settlers from England, Wales or Scotland who moved to Ireland in the 1600s probably as part of the Plantation. So that could account for the “even after being there for over 200 years” reference.
Native Irish were almost invariably Roman Catholic, whilst the setters were mostly Episcopalian (Church of Ireland), Presbyterian (in the case of many Scots), and a mix of other smaller denominations eg many Quakers moved to Ireland for commercial reasons. There were some Catholic settlers but in the main your denomination marked out your probable origins. And still does to this day.
The relationship between the incoming English, Scots & Welsh settlers and the native Irish was not always totally harmonious, you might say. People don’t like having their land taken and new ways of life forced on them. (Ironically, that history appears to have often been forgotten when Irish people later moved to north America and similarly settled lands there belonging to native Americans, who also resented losing it and being forced to adopt new ways of life).
As to whether your ancestors were “good Irish”, I am sure that’s not something I know a proper formal definition for. You say there are many newspaper articles saying your ancestor was a very good, generous and friendly man. I’d say that speaks volumes about his character and background. He sounds a good Irishman to me.