My order finally went through around 1:30PM (central). Been trying since 7:30AM.
Also concerned about the "iPhones can only be shipped to AT&T billing address" nonsense. Um, hello, AT&T -- most people aren't sitting around at home during the day, waiting for a SIGNATURE REQUIRED delivery!
Went back to apple.com order status and changed the shipping address to my work location. A bit concerned that this will hose my order. We'll see.