I went from the LI Sound down the east river (and back) for the first time this past June. All the info you got is spot on.
I just want to second the comment regarding the traffic around the South Street Seaport and the Battery. Plan on lots and LOTS of traffic, some paying attention, some not, some being courteous and some not. At one time I was staying to the right side of the river (heading south) and getting passed by a water taxi. A circle line
boat was heading north in the middle of the river. Just as I was passing the Seaport, a large 3 master schooner let the dock right in front of me, leaving me VERY little room.
There will be water taxis, tour boats, tugs with barges, private boats, police boats, coast guard vessels, helicopters, etc. And the worst seemed to be the Staten Island Ferry, which moves at a high rate of speed and in a straight line
and did not seem to move for ANYONE.
Time it right and you'll be through in an hour or so. Have someone take pictures and enjoy the sites but the helmsman better pay attention front, sides, and rear.