Same exact story happened to me, this is uncanny.
I got my replacement yesterday but I had to drive all over the state just to find the exact red one since all the nearby AT&T stores were sold out.
So I got my fresh unit in factory default, loaded my backup from the bricked one, but this time, I did not install any apps except for a few I use (Twitter and Rdio) so I could determine if apps were causing the background battery drain of my first unit.
But I actually installed and used Nokia Drive last night after getting it because I had to use it to get home (the AT&T store I drove to get the phone was in a a neighboring city I don't frequent.) I blocked Nokia Drive from background tasks after this.
So I charged my fresh phone overnight from zero, and today, it's been two hours since I unplugged it and it's still at 100%, I did a bit of the people hub, a FB video, some email syncing. I have NFC off, Cellular Data on, WiFi on, a bunch of emails syncing manually and no background tasks. But I don't have much apps and no third party Live Tiles yet.
But with this fresh start, my battery is holding excellently and my 920 is cooler unlike the first unit I had (the one with tons of apps installed).
I'll use it regulary and monitor it today but so far, things are looking up and much better.