I've spent many, many, many hours in both Harriman, Sterling Forest, and the private land between the two, although I haven't hunted any of the three areas. I disagree that the habitat of Harriman has been trashed by deer. There are some parts of Harriman with low plant/animal diversity and some vibrant areas with a wide range of species. In my experience, the areas with low diversity are predominantly in centers of human interference on the landscape. You can't blame the deer for not eating plants that have proliferated because of people.
Mountain laurel thrives in rocky, mountainous forests with acidic soil. Harriman is a rocky, mountainous forest that was heavily mined in prior centuries. Many areas were clear cut and the wood used to feed the furnaces. Between the erosion from the logging and erosion from disturbing the rock, any area close to a mine has very acidic soil. Acidic soil limits the nutrients available to plants, stunting and sometimes stopping root development. Of the 36 official bodies of water in Harriman only 8 are unaltered - 28 are either damned for enlargement or created totally from scratch. This redistribution of water within the park has had a huge impact on the soil. On top of all this, ML is toxic to deer.
The proliferation of the Japanese barberry has little to do with deer and much to do with Japanese barberry and people. JB is an invasive species brought to the US by people. It grows its leaves earlier and sheds them later than many other plants and so it enjoys a growth advantage. The seeds have a very high germination rate and are heavily dispersed by birds along the powerlines. JB will thrive in woodlands, wetlands, swamps, meadows and disturbed areas (just about 100% of Harriman). When JB starts to grow, it lowers soil acidity and creates a more favorable growth environment (that it already has a head start growing in!). With the cards stacked in favor of Japanese Barberry in Harriman, It's flat out wrong to blame deer just because they don't eat the stuff.
Between the gas pipelines, electric pipelines, and the summer camps, there are many areas where the forest is removed and barberry/mountain laurel are the fastest-growing and hardiest plants that fill in the gaps. If there were zero deer, then there may be a wider diversity of regenerative plant growth in some or all of these clear cut areas. However, then there would be zero deer and less diversity elsewhere. I agree that Harriman could use a "habitat restoration" but I have no idea how this could be achieved.
In Sterling Forest, the areas most heavily grazed by deer are now characterized by an overgrowth of fern species while the clear cut powerlines are filled with laurel, barberry, and other thicket species. In my experience, Sterling has much more coyote and bear (generalists) activity than Harriman and borders on overpopulation with these species in some areas. Harriman has more bobcat (specialist) activity and a greater balance of predator species, even extending to a greater diversity of predatory birds. The private land between the two parks is in the worst shape ecologically and will probably be developed at some point soon.
I agree that more hunting would be great for the hunting community but I disagree that deer have done anything to ruin Harriman. Amongst many local non-hunters, I do get the sense that Harriman is theirs to be "protected" while Sterling Forest is ignored or looked at derisively.