Fuel....Cheapest fuel in three states is at Atlantic Highlands, also can stop at Liberty Landing next to the statue of Liberty
If what you wrote is that you are arriving at NY harbor at 12 midnight, Id go down to Atlantic Highlands and await the tide change. Leave there at 6 AM and you will sweep up through the NY Harbor and then East River with the current to the LI Sound by noon. Current starts running against you at 11:30 PM June Ninth
Hell Gate is not as imposing as you think, just want to not run against the tide that's all. The tugs and barges general run 1 hour either side of slack tide so I would avoid that. As you turn the corner from the East River to go through Hell gate just give any other vessels in that turn room.
Looking south through Hell Gate. In the distance is the East River bank
Roosevelt Island close to Hell Gate..note SOG. we have hit speeds as high as 13.4