Any advice you have on how to speed up a shipment from AT&T would be great.
There isn't any way to speed up delivery but I can tell you how to get it sooner.
If you have your phone ordered and locked in for delivery through a contract and subsidized price, you're going to have to go back to the store you ordered it from and cancel it.

I know, I know, crazy right??
Once you cancel it in the system, go to the Apple website and go to the iPhone link. Hit "Buy Now" and select the model you want and the carrier associated.
Once you do that, just below phone you'll see "check store availability." Hit that, put in your zip code in the popup box and you'll see your surrounding stores. Most of them will show "unavailable for pickup" but you may hit that gold nugget. The absolute best time to check is right after midnight but I tried my luck 2-3hrs before store opening and got success.
I just did it yesterday but couldn't lock it in because I didn't cancel my order with ATT as my contract was locked in to that already ordered phone. But today I did it and tonight I have my iPhone 6 Plus 64Gig in my possession.
A couple of caveats.. if you're willing to drive a little distance (only in case its mandatory) then this may be more viable for you.
I had the same delivery date and I didn't want to wait so long.