The lower altitude is also a minor issue, since there is no guarantee of higher-altitude use which would allow military missile-launching so close to airport traffic. As I said before, the military has a great deal of airspace designated for their own use well away from commercial airports. Of course, it could have been an accidental launching during transit, but this seems somewhat unlikely.
The Hamptons are about 80 miles east of JFK. Saying this is "so close" to airport traffic is rediculous. Since you're a (Wow! An IFR rated) pilot, why don't you have a look at the New York Sectional and tell everyone what the legend says that is printed just south of where TWA 800 fell.
ML/NJ