
Re: "Just so you know, I’m very skeptical that “Irish naming patterns” are a strong argument, especially once they get to America. And every Armstrong had a William"
It's the birth order that matters here.
I've seen Irish naming persist for three generations in the US, if the persons involved are all Irish. For people born in Ireland, unless they're one of the weird ones (e.g. my Lithgow ancestors, or those who married Englishpeople, like my Wright ancestor) they stuck to this in the US. Marrying a woman of Welsh descent would therefore put this into question, so yes I agree with you that we cannot count of their naming choice for first-born son to absolutely agree with Irish tradition in that case. Had James married a Irish immigrant, though, I would have been shocked if they *hadn't* gone with William, even in the US. ;-)
I have peeled away my unknown wife and son from James now. Thanks!
FWIW, after re-analyzing my top-200 DNA matches, I have yet to find any that are descended from the Paxtang Armstrongs. These may be related to me but it's clearly more distant than John of Brookeborough. Without any kind of DNA guidance I'm quite comfortable leaving them disconnected as of now. If they did come from Ireland it would likely have been from at the closest a brother of John, although once again with DNA this might just be the luck of the draw.
I have two (non-DNA-related) Armstrongs with whom I have no DNA overlap to place, who had been glued into the Ireland tree without consideration as to any kind of locational affinity. They likely will need the same treatment - probable Irish origin, but also probably not descendants of John. I'll post them here for later reference:
James Armstrong
Thomas Armstrong