I have to admit that I'm not current either, but we're talking about 1996 here.
I don't think these things change much. Look just south of the Hamptons about five inches to the area the bottom of the chart just east of 72-30. Read the little legend there. (I'll give you a clue. You can see what it says at my "It wasn't Terrorists" post that was previously linked on this thread.)
ML/NJ
Although I do not know for sure, I assume that the flight was to intercept the 236 radial at the East Hampton VOR. From everything that I have looked at, the flight never strayed into the warning area W-106.
Given the shear amount of traffic that make that same track out of JFK, not to mention La Guardia and Newark, I cannot see how the Navy could fire any missile in the area without hitting SOMETHING.
I am not necessarily disagreeing with you or UCANSEE. I just point out that that I need more than uninformed speculation to convince me. And I don't see much informed speculation.