Finally!
It took a while but I was finally able to order a 32GB iPhone 4 from the Apple Store. I've been at it, off-and-on, since 10 AM PT but it seems like ordering from the Apple Store is your best bet right now (I can log in to my AT&T Wireless account but I cannot "upgrade" my current phone). Anyways, my new iPhone 4 is scheduled to arrive at my house on June 24th.
For those of you wondering, if you're an existing iPhone customer with an unlimited data plan (EDGE/2G or 3G) you will see the unlimited data plan listed for $30/mo as an option when selecting your data plan.
For us poor schmucks living in California, we have to pay sales tax based on the full price of the phone ($699 x 9.25% = $64.66 sales tax... ick!) so my total came to $363.66. Seeing how I was going to upgrade to a 3GS back in April, I'm kind of glad I waited.
Edit: Forgot to add, I don't see the AT&T $18 upgrade fee. Maybe it got waived, maybe it didn't. At this point, it doesn't really matter.