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)