You've ruled-out the known spotty LTE switching/searching issue, I'd perform these additional experiments:
1) Disable iCloud sync entirely for a day. In iOS5 there used to be a bunch of battery life problems caused by devices getting caught in an endless loop of pointless background syncing. Maybe you're still hitting something like that.
2) Turn of location services for a day. Maybe you've got something like Find My Friends taking up too much juice?
3) Turn of email "push" for a day. Maybe you've got too many email accounts?
Failing that, maybe you've got a dud? Take it to the Apple store and they can look at your device energy usage logs. They'll most likely tell you to do a fresh iOS install suspecting a software issue.. but in the end they might just switch you to a new device.