As you say there are a number of parallels.The most interesting is that James Agar (1815-1881) had a half brother, Henry, born of his father John's second wife, Nancy. As near as we can figure, John's first wife, Mary Bailey, died about 1821.The children of the second marriage are listed in my principal source, and article on John Agar (son of James who came to NJ).John said that his father's half siblings were: Thomas, Henry, Annie, Margaret, and William.
The Agar family was Church of Ireland (Anglican/Episcopalian), but Mary Bailey's family was Methodist and I don't know how the children were raised.James joined the only nearby church when he came to NJ, the Northfield Baptist Church.
The name Agar normally is derived from Elgar, the El from eld or old and the gar meaning spear, as in garfish.Ireland has a lot of Agars, suggesting they may have come over early, perhaps even in Norman times.
I don't see the name Agar as that common in Carlow,and nothing at this point rules out Henry and James as half-brothers.The dates fit, since Henry would be rather younger, but old enough to emigrate.
The Protestant Irish were the first to emigrate because they had more money, they were under pressure from their poorer Catholic neighbors, and they were generally more willing to move on.things were turnng bleak in the 1840s, so many left.
I expect, remarkably, to be in Carlow and Knockullard early in May, and may (or may not) find something out when I am there.Mostly at this point, I just want to see it.