Craig,
A little southwest is obviously Fresh Meadow, but I think you are asking about what looks to be three greens on the Grace estate called Tullaroan that later became the grounds for Deepdale's relocation in the mid-50s.
http://www.oldlongisland.com/2011/01/tullaroan.html
On that site, there appears to be a circular green and two other diagonal Redan-looking greens, but I also see a few trees among them. Could it have been a three hole practice course? The owner J.P. Grace was married to C.B. Macdonald's daughter Janet after all. Perhaps a wedding present?!
Bret,
Years ago, I walked the location of those three greens in the NGLA range. Too bad they were sorta washed away over time.
Creek had a version in their range until the recent renovations and they appear to have been incorporated into a larger feature.
Nigel,
I wasn't trying to suggest Bahto's book got the three hole course wrong. Macdonald says as much in that passage.
I do wonder just how many more of them were built. I suppose if people didn't build them by 1930, they didn't get built at all.
I'm always trying to convince some friends of mine to build a version of it on the properties of their rural weekend homes.