According to some both Roger Barton and Robert Bloomer were expelled by Governor Nicholls of New York from Brookhaven, Long Island (Seatucket?) and fled to "Connecticut." Rye, NY was once considered to be a part of Connecticut.
I have heard of the Bloomer book and had glanced through it once or twice.
I descend twice from Robert Bloomer. One of my maternal great(5) grandmother's was Mary (Bloomer) Ogden, wife of Jonathan Ogden, a UAE Loyalist from North Castle, Westchester County, NY. Mary was a daughter of Gilbert and Phebe (Shewrood) Bloomer of Rye, NY. Phebe (Sherwood) Bloomer's mother was also a Bloomer. Her name was Elizabeth Bloomer, wife of Joseph Sherwood of Rye.
I know that Gilbert was a son of Robert and Elizabeth (Sutton) Bloomer. I suspect Elizabeth was a daughter of John and Elizabeth (Boyd?) Bloomer (not sure).