I found some interesting things in a book called
The Iconography of Manhattan Island. It's a multi-volume book with some history, early maps and prints depicting NY Harbor.
Does anyone else know this book? Would those images be useful?
It also says that when Stuyvesant first established government in 1652,
"The jurisdiction of the burgomasters was fixed as 'between both rivers
[Hudson and East Rivers] and as far as the Fresh Water.'"