Ok, it would appear today I talked to a Premier rep that actually knows what he's doing. My guess is that AT&T staffed up with a ton of temps to handle the volume, and for the first time since I've been calling, I actually got to a real employee.
He read through all the notes on my account, said there is no reason it shouldn't have gone to processing already. Then he said the magic words "I'm going to process this order manually so that I know it will go through correctly". Placed me on hold for about 15 min, checking in every 2 minutes to tell me where he is in the process.
20 min after I got off the call, my order is now showing in the main AT&T system as backordered, 6/25. This guy was sharp, polite, and gave me the proper attention as a Premier customer. He just did what he needed to do to get the order into fulfillment.
Hold times are very tolerable today after the first wave of orders and activations have happened. I'd guess another week or two for me to get my phone, but at least I can see both of my orders are in the fulfillment system.