I might just get up and go.
Check Eldridge, see what's doing with the tides in the Sound. Mid-sound they are often very different from shoreside, sometimes you will even see them reversed so knowing whether to go shoreside or mid-sound makes a difference.
When you get near the Throgg's Neck bridge, check again. If you're not making much progress, or need sleep, there's a general holding anchorage in Little Bay, just SE of the bridge by the USCG station. You can hang out there if you need to. There are a number of odd little anchorages
charted in the approach to Hell Gate, don't be afraid to use them.
As for the HG itself....max current through there rarely exceeds 6 knots, so with a 35' boat and a little wind
, you should be able to motorsail if need be and keep on pushing through. If you figure it can take 2-3 hours to transit the HG, East River, and round the Battery
...no matter how you time it some part will be against you. You can get some odd square waves in the East River, and odd wind shadows from the buildings, so foulies and securing the hatches might be advised.
But if the key word is "ASAP"...break on through. The worst that can happen is that you'll be stuck in one place making no forward progress at the Hell Gate for 3-4 hours if the current is too much for you.