I am close to certain that my JS was William's son. The dates and locations are just right.

I found a Margaret Underhill, but have not been able to confirm her since I don't have enough detail,

There's an interesting site that records family Bible info from Oyster Bay. Have you seen it?
http://www.rootsweb.com/~nysuffol/biblerec.html

On mytrees.com there is a good tree for Harriett, JS's wife. Her maiden name was Long. There's a big connection to the Brasher line.

Do you have dates and places for Henry? Do you have a middle name for William or James T?