With respect, you guys know very little Irish/Irish-American history and it's obvious from the terminology you're using. First, as a preliminary, there were Irish (or what's being termed here as 'Irish-Irish') in the British colonies since the 17th Century, before the pilgrims even. 800 people from Ireland and England were planted in Virginia during the period of British settlement before 1620. In 1621 Virginia, there was an Irish colony of Cork origins, at what is presently Newport News, that was planted by a Sir William Newce, who sailed on the Flying Harte. In Hotten's Original Lists -- a valuable source for 17th Century genealogy -- there exists a notable quantity of traditional Irish names. In New York, one of the first provincial governors of the colony, an Irishman Thomas Dongan, had requested more Irish settlement in 1682, and so followed during the proceeding years. There are genealogical records and preserved documents for New England, Pennsylvania, and the various other British-American provinces which show similar patterns. That's number one.
Second, you are confused on a fundamental level with respect to both 18th Century migration patterns from Ireland and the sociopolitical conditions that existed on the island at this time. It is true that 17th Century Irish settlement in Colonial America was light and sporadic, but this changed by the 18th Century when Irish ships bound for the colonies embarked with increasing regularity and carried with them copious supplies of new settlers, starting in 1718 and waning by the time of the Revolutionary War. During this period -- 1718 - 1775 -- there were three generous waves of Irish migration that have been noted with distinction, surrounded by smaller but frequent arrivals from the isle; the best estimates place the total number of Irish arrivals for the 18th Century on the order of 250,000. Of this number, about half left from Northern Irish ports and the other half took ship from Southern ports. Very simply put, only 50% of the 18th Century descendent and born-Irish colonists came from Ulster while the other 50% came from Ireland's Southern provinces. Of the Ulster half, a significant minority came from the three counties presently in the ROI -- Donegal, Monaghan, and Cavan -- which were not planted with Scottish and English settlers. From the remaining six counties there was a small minority from the stock of the indigenous population, which further reduces the number of settlers who could've claimed ancestral origins in the Borderlands. Or to frame this another way, less than half (and probably less than 40%) of all 18th Century Irish immigrants were Lowland Scottish or Northern English in ancestry.
There was no deliberate attempt to wed Irishness with Catholicism until the mid-late 1800s. During the 18th Century, most of the indigenous Irish were adherents to Catholicism in only weak and superficial ways -- and as a matter of fact, when Catholic piety reached its European peak in the Middle Ages, it wasn't uncommon for Romanists in England and elsewhere to rebuke Irishmen for behaving more like atheists and pagans than Christians. The Reformation failed in Ireland not because Catholicism was woven into Irish patriotic identity (ironically, the framework for Irish Republicanism was laid mostly by English-speaking Anglicans) but because the Protestant clergies failed to incorporate the Irish language into their religious doctrines, and it was the Irish language that was widely spoken by most of the indigenous population, including the Norman-Irish gentry. Most of the 18th Century Irish came to Colonial America as Catholics, but due to a combination of a scarcity of RC churches in the colonies, de facto bans on Catholicism in some of these colonies, and the regular disparagement of Catholicism in most of these colonies, not to mention their already soft adherence to the faith, the 18th Century Catholic Irish (or what you call 'Irish-Irish') converted and joined the local Protestant churches. By the turn of the 19th Century, most of the Irish in America were Protestant, and most of these Protestants were "Irish-Irish". What happened was a process of cultural assimilation -- that was both linguistic and religious in nature -- that took place in America and was distinct from whatever sectarian divisions and obstacles to social cohesion may have existed in Ireland itself, and regardless of how prominent or not these barriers may have been at the time.
"I know this can be a difficult subject, so as someone with both Irish Catholic and Ulster-Scots Protestant genes,.."
I know of no religious genes that have been discovered. As I've been saying, the Protestant Irish of colonial and antebellum America were mostly Irish. Even most of the Ulster settlers of Borderland stock considered themselves to be Irish until an influx of Catholics from Ireland arrived during the Famine. After the US Civil War, sectarian tensions in Ireland heightened, and in America this same perception of Irish-Catholic interchangeability took form. It was during the late 19th Century genealogy craze -- when it was entirely unfathomable to imagine any Irishman a Protestant -- that the phrase "Scotch-Irish", made popular by the Scotch-Irish Congresses, started to be thrown around with frequency and used to describe anyone who was a Protestant descendant of Old Stock genealogy and who came to America by way of Ireland. The problem with their best efforts, though, was their ignorance of immigration history and their lack of familiarity with surname origins; which is why we see, throughout the literature of this period, any and every Irish Protestant assigned the "Scotch-Irish" misnomer, regardless of whether their names were Cullen and Sullivan or Brown and Jackson, and the folk belief that they were all 'Ustermen'. In recent years, "Ulster Scots" mythologists have been at it again, only this time preferring the title "Ulster Scots" to "Scotch-Irish" and making brazen attempts at trimming the "Irish-Irish" Protestants off their roster of heroes -- and with them the better part of Protestant Irish-American history. It is for this reason, as a genealogist, that I don't consider the Scotch-Irish (or the Ulster Scots, or the Ulstermen, or the Ulster whatever they imagine themselves as next) to be a serious ethnoreligious class deserving of the unique acknowledgement they demand.
I also know of no genetic genealogy project that has discovered unique Scotch-Irish genes in the biological makeup of people who identify with this pseudo-ethnicity. As far as I am aware, the largest of these projects is being conducted at Family Tree DNA, and they have over 1,200 participating families last I checked. The genetic profile of these families is as follows,
" R-L21 Haplogroup and the growing number of downstream (more recent in chronology) is the haplogroup of the majority of the Scots-Irish. Historically it represents the 'Western Atlantic Celtic' population, which includes the Insular Celts, both Gaelic and Cumbric. In layman's language, this population has its origins in the indigenous Celtic tribes of Britain and Ireland. Within the Scots-Irish population this includes the native Cumbric Celtic tribes of what we now call the Scottish Lowlands, and the Gaelic population. This tells us the majority of the people in the New World that identify as 'Scots-Irish' are the descendants of the indigenous Celts of the British Isles and Ireland."
You're not going to find a genetic profile any different than this among the 'regular' Irish. The R-L21 haplogroup is found nowhere in the world in greater frequency than Ireland.
"Us Scotch Irish maintained a careful distinction between "us" and the real Scots (the real Scots came early to New England, for instance, as Cromwell's Prisoners of War). The real Scots were Gaelic speakers, often (but not always) from the Highlands, tartan wearers, etc."
Around 35% of the Ulster Scotch-Irish 'were' of Highland ancestry. Some of the most popularized Scotch-Irish surnames -- Campbell, McCain, McDonald -- are Highland in origin (note that I don't even believe there is such a thing as a 'Scotch-Irish' surname, but I'll play along to make the point). There was significant settlement of Highland Scots in Ulster during the 1500s, a century before the Plantation, and most of these families joined the reformed church movement and then the 18th Century migrations to the New World.
"Barnes is an Irish-Irish name, an Anglo Irish name, a Scots Irish name."
I have no idea what an "Anglo-Irish name" is. The Anglo-Irish were the upper and bourgeoisie social classes in Ireland from the Tudor period until the 1922 partition, noted for their political power; adoption of English customs in manner of speaking, dress, and living standards; and of course their Anglican religion. Some of these families were ancestrally Irish and converts to Anglicanism (no less than 5,500 Catholic Irish converted to Anglicanism when the penal laws were instituted, not including the early converts from the Tudor conquest), some were the descendants of English and Welsh Cromwellian and post-Cromwellian settlers, but most were mixed Irish-British. This is not a single ancestry, and the closest thing I can imagine to an 'Anglo-Irish name' would be a name that falls on some hypothetical list of the names of the members of this social class. Those names would be either Irish, English, Welsh, or hyphenated to reflect their mixed Irish-British ancestry. There were a lot of Fitz names held by these people (which, depending on the name, could be Irish or English), as well as names like Burke, Sheridan, Connolly, and the hyphenated Connolly-Carews (the Connollys, who were by far the wealthiest of the Anglo-Irish class, had intermarried with the Welsh Carews). Some of the more prominent members of this class bore Irish or Norman-Irish names, but were intermarried with English aristocratic families (the Dukes of Leinster, the Earls of Upper Ossory, the Guinness family, etc).
I would recommend most of you read some proper scholarship in this area instead of just repeating the various zombie claims that float around unchecked in 'Ulster Scots' heritage circles. Michael P. Carroll published a relatively recent study on the Protestant identity of the American Irish, which you can read here,
https://books.google.com/books?id=PQh3pTgmRJ8C&pg=PA1975&lp...
I'll close on an advertisement. I am currently constructing a website that will feature much of my genealogical research. The subject is Irish-American genealogy, and the focus is on the colonial and antebellum periods. The aim is to amass a large database of family histories for the American Irish, which is going to require participation from ordinary Irish Americans. Please feel free to contact me if you want your personal ancestry featured, and I will even consider publishing a separate piece on your family history, under your instruction.
Best of luck in your efforts.