THIS FIXED MY BATTERY DRAINAGE ISSUE:
1. Sync iPhone to iTunes. Sync contacts in iCloud.
2. Do a DFU restore, procedure and description can be found here and here. Make sure to setup as a new phone. This will take at least an hour, possibly more depending on your download rate. It will also wipe your iPhone settings, your music, photos, a good portion of your application data, etc. So you'll need to spend some time afterward restoring these.
3. After you restore as a new phone, sync with iTunes to restore your apps.
4. Unplug and let your battery drain all the way. If your bluetooth is off, turn it on; go to youtube (in Safari), find yourself a free movie, and let it run. The point is simply to deplete your battery.
5. Charge overnight, all the way to 100%. Keep it plugged in for a while - I unplugged mine after a total 7 hours of sleep.
My iPhone was back to normal after steps 1-5. Yours might be, too. If all looks okay, restore all your app data, music, etc.
7am this morning my phone was charged to 100%. 2 hours usage + 16 hours standby later, I have 63% battery. Usage was Safari (WiFi and cell network), Maps, a few apps using location services, etc. Notification center has Weather, Reminders, & Calendar. My phone is legitimately back to normal.