Mark:
Phil Young is right; the best thing to do and perhaps the first thing you should do is just contact the club and ask them if someone there could explain their architectural history to you.
There has been a contributor on this website, Chip Oat, who belongs to Rockaway Hunt or did and he's very good on architecture and may be able to help.
As far as Cornish and Whitten, some years ago I had a long talk with Mr. Cornish about how they researched and compiled their wonderful architecture history tome, and he said most of it was just constacting the clubs and getting them to provide it. I asked him if they got it wrong then his book would list it wrong and he said generally speaking of course that would be the case.
I remember Rockaway Hunt from the old days when I grew up on Long Island. The club had a very interesting and unique ethos and membership policy back then and maybe they still do in that they took in lots of playing members seemingly on a temporary basis who were guys sort of coming through the whole Wall Street and financial world in New York particularly if they were from other states or other countries and sort of passing through temporarily. The club was unique that way and we got to know a lot of those guys while they were around NYC before migrating out or back to wherever they came from or were going.
The club is very old and the bones of the course are too, I think, so it should be an interesting research subject for you.
And SBendelow offers some good leads via the old magazine articles he listed for you. If you can get your hands on those at least and present them to Rockaway Hunt it's certainly possible you may be showing them something about the history of their club or course they may not be that aware of at this time.