Mr. Sweeney;
I'm not very knowledgeable about the architectural lineage; I seem to recall reading somewhere the architect was Robert Trent Jones.
I do know that this is not the original location of the club. The club's original location was in the Douglaston section of Queens, not far from the Cross Island Parkway. As real estate closer to NYC became more valuable, the club sold off land and moved further east, into Nassau County. The original architect was William Tucker, if my sources are correct.
The original course is not entirely intact; through time, it was modified, to what degree and on what holes I am not certain, but am certain that today it exists as city-operated Douglaston Park Golf Course.