|Lange Eylandt, cropped from a Dutch map.|
In the 1650s-1670s, Johann Polhemus ministered at the west end,
in Brooklyn, while Mary Dyer spent the winter of
1659-1660 on Shelter Island at the east end.
I doubt that there was a direct connection to William or Mary Dyer, but Polhemius was a beloved and well-respected minister in the New Amsterdam society. He was one of the ministers who, in 1658, reported that "The raving Quakers have not settled down -- for altho our government has issued orders against these fanatics, nevertheless they do not fail to pour forth their venom. There is one place in New England where they are tolerated and that is Rhode Island, which is the caeca latrina ["bowels latrine"] of New England." (Really, the cesspool? That's not very nice to say!)
Polhemus' children and his widow would almost certainly have known or come under the influence of the New York mayor, Major William Dyer, 1640-1688. Yes, the younger William, who obtained his mother's reprieve from death in October 1659. At the risk of placing that earworm song "It's a Small World," in your brain, I urge you to read: