Since I last wrote, we have gotten confirmation from my ggGrandfather Patrick McQuillian's naturalization papers (it was spelled McQuellen on there, McQuillan on censuses, and many other variations thereof). He was born May 1, 1846 in Co. Monaghan, Ireland, and arrived in New York City June 1863 at the age of 17.
His marriage record (he was married in 1866) specified his parents as Patrick McQuillan (sp) and Bridget (unknown). We also have censuses for himself and family, though we are less sure the Edward McQuillian in RI at the time was related.
He died here in Rhode Island, although we can locate no death record or grave.
It does sound as though there is some possibility he may have been the brother of your Philip and James, though it's hard to tell when we both only know the county.
I am visiting Ireland in a couple of weeks, and am hoping to make it to Monaghan, I will follow up if I learn any more...