So I FINALLY got through to someone from Premier on the phone, and was able to correct my billing information (they were trying to put my CC through using my shipping/work address, which is why it failed.)
The CSR assured me that I won't lose my place in the queue -- he saw, correctly, that I had ordered the phone "3 days, 3 hours, and xx minutes ago." He said that is the queue order using for shipping and I should still be OK. Heck, even if it doesn't come on Friday, if it comes Monday/Tuesday I'll be thrilled. I'm also a short hop from the UPS/Fedex hubs in Louisville and Memphis (I'm in Birmingham, Alabama) which might help my chances.
Just got off the phone with him 5 minutes ago, and so my order status hasn't changed yet, nor have I received another confirmation email. I'm going to try and be patient and not refresh the order page every 30 seconds. 😀
But maybe, just MAYBE, I've avoided having to go stand in line on Friday. (fingers crossed)