The preorder page says I won't be charged until the product is available. Does that mean when it ships? My card expires in November, which is almost certainly before the game ships.
You will be charged as soon as the beta is available. You will not have to pay anything for the game after that. So you can go ahead with your pre-order.
Actually this whole we-will-charge-you-when-we-ship is kind of annoying.
This is not how it is going to work. Where did you get that information?
Quote from the pre-order page (after you click "Add to cart"):
NOTICE: Your order contains at least one Pre-Order item that will not be charged to you at this time. You will only be charged for the items in your cart that are available at this time. Your preorder will be saved in our system, and when the product becomes available, you will be charged and notified.
Beta = becoming available