Would you be able to confirm how you are testing this? If I set my default shipping address on my account to a US address with a Zip code of 10005 (new york zone 4 for you), I'm shown a price on your priority mail method for zone 4 in the cart, without setting my address on the cart.
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However looking at it today it seems correct, other than on the catalog items for sale where it shows zone 8 price with a ~ in front?