If you use Sunday June 23, 2013 as an example. ( full moon)
According to Eldridge
High Water at the Battery is listed as 8:38 a.m.
The Current in Hell Gate turns to the southwest @ 10:26 a.m Approximately 2 hours after the high water at the battery.
If you look at pages 128 thru 133 in eldrige they give you graphical diagrams of the current in 1 hour increments. Based on those diagrams @ 2 hours after high water at the battery, you'd already have 1.8 kn (sw). @ 3 hours after high tide at the battery you'd have 4 kn. (sw)
According to this current diagram slack is about 10:25 a.m:
Hell Gate (East River), New York Current
So, if you wanted to be at the gate At slack in the gate, you could leave the throgs neck about an hour after high tide at the battery. ( the current turns there 1 hour before the gate, so you'll get a push to cover the 7 miles.)
As you proceed down the river you could be catching up with the turns which occur later and not taking full advantage of the sleigh ride.
I believe, the 2 hour departure from throgs neck is designed to take full advantage of a favorable current and not neccesarily hit the gate at slack. ( I'm sure someone will correct me if I'm wrong)
So, I believe it depends on what your goal is.
If you're destination is Liberty landing marina, you could hit the gate up to 4 or 5 hours after high tide at the battery and still get a favorable current. It's only a 2 hour trip with the current..and maybe another 1/2 hr to cross the hudson to the entrance to Liberty.
For those that are proceeding further south, the goal would be to hit the gate as early as possible to keep the favorable current down past the Verrazano narrows and beyond. On June 23rd, for instance, the flood at the narrows begins @ 4:34 p.m. You'd want to be through and past before that turn.
If you're heading up the hudson, you'd want hit the gate later to catch the flood up the hudson.
The last time through for me, I got to City island from port Jeff too early to head down river..so I took a leisurely siteseeing trip around Hart Island to kill some time. I didn't realize that it was the potters field for NYC and that the prisoners from Rikers are the burial detail.
I ending up hitting the gate at slack that day, I had never seen it so calm. But as Rich stated I encountered a Tug and a Barge that I slowed to let pass me earlier at the throgs neck, still turning in the gate. So I just backed down and let it clear.
Rich mentioned keeping and eye around corners. One of the spots to keep an eye in is the main channel around North Brother island. Most small craft will take the channel between the brother islands (at least, I do) . Once you emerge in either direction, you should look to see who might be coming around from the main channel.