Basically, with New Year's Eve you have to forget about the strategy of waiting until the last minute. The people who've already commented are right that prices don't drop, but what usually gets overlooked is that hotels don't even maintain availability to speculate. By mid-December they're already almost fully booked, and what's left are the most expensive rooms or the worst locations, at prices even more inflated than in September.
The key point here is that New Year's Eve isn't like other tourist dates. People plan this way in advance and hotels know it perfectly well. If you see offers 6 months ahead, it's probably because they're interested in securing occupancy, but that doesn't mean the price is going to improve later. On the contrary, as the date gets closer, prices go up because demand is pretty much infinite and inventory drops like a stone.
The most realistic approach is to book between 3 and 4 months before if you want some flexibility in choosing. That gives you enough time to have decent availability without it being so early that you're betting on amazing deals that probably won't exist anyway. If you wait until October or November, you're probably already paying top dollar or seeing very limited options. So yeah, in this case it's worth biting the bullet beforehand, even though it hurts.