If my memory serves me right, New Jersey laws don't allow motorists to take their deer...they're actually required to get a permit first.
Also, wasn't PETA the group that forced the state to restrict the length of the hunting season several years ago, because the hunters were presumably taking too many deer? All I remember was the silly "deer contraception" program they proposed as an alternative for herd management. Does anybody else remember this? It was 8-9 years ago.
About 1970 it became a wildlife preserve in order to prevent it from becoming a huge airport serving New York City. A bunch of left wing nuts started running it there were huge fights over hunting. The deer population swelled. Lots of corporations built sprawling office complexes with lots of greenspace and ponds. The deer and the geese love it. My dad lost hundreds of dollars of plants and trees. I've almost been hit by deer twice. When I visited in the early 90's I would see a couple of dead deer along the side of the road each trip.
I remember they were trying a deer birth control plan a few years back. They tried mixing birth control medicine with feed. They couldn't get it to work. Different deer would get a different amount of feed and they couldn't find a birth control drug that would work.
They then demanded that the state hire enough workers to trap, radio collar and give a birth control drug to every female deer. It would have cost 100"s of millions of dollars. It was never implemented. Since my parents moved out 3 years ago I don't know what there doing now and don't care.