I don't have anything to contribute to this fascinating thread, except maybe to try to clarify about NJCF (New Jersey Conservation Foundation). As far as I understand it, NJCF is a private not-for-profit organization, which acquires land to preserve it. They do get public funding - NJ DEP Green Acres, for example, as well as private donations. But the land they buy and own is not public property. It is private property, and they get to decide the rules for access. They do in fact open many of their properties to public access, including hunting, but that's their call.
This might result in some confusion when looking at maps. NJCF properties might be shown as "open space", "preserved land", just like state forests. Because they are. But they aren't public property like state forests. You and I can only go there if NJCF permits it.