Like others have said, you do get things opened up early for booking as a Haven member, but I have noticed that their IT guys aren't the greatest, and sometimes you simply can't book the reservations. I strongly recommend calling the concierge line ahead of time, they will take care of things for you and are easy to deal with. Once you're on board, get to know the concierge, he can work miracles. That said, be kind to the concierge. He can work more magic if you're nice to deal with! We've had plenty of luck getting into sold out restaurants and shows.
Also, like others have said, book Teppenyaki early, it does fill up and it's trickier to shoehorn people in due to the seating arrangements and popularity.