We have done the Cape May-Montauk ( really Block Island- Great Salt Pond) several times in our previous sailboat, but never in the GB. Prevailing summer winds are southwesterlies, so seas should be on the stern. Commercial traffic is not too bad, although you cross the traffic lanes to New York. I would not recommend Shinnecock, as it can become impassable on a strong onshore wind. Plus, you would have to exit the inlet and continue up the coast, as there is no way out of the bay (I would not attempt the Shinnecock Canal in a large boat). There is nothing really scary about running at night, there is not much to hit and the ships are all lit up. In our GB, we have always run up the Jersey coast, or if a strong north easterly came up, run up Barnegat Bay. Takes two days, but not a bad trip.
Good luck on your trip.
Roger and Anne