Will be interested to hear if your phone stays fixed especially as I often run some of the apps you mention.
My 4S had been suffering with terrible battery and has been running warm in my pocket when it should be in standby since some time after upgrading to 6.1.3. My standby and usage times are almost the same values and yet my phone is barely used during the day except to receive emails from icloud. Following it also consuming my monthly data allowance (which has ****** me off), and having tried all other things like disabling iCloud functionality I decided to take the drastic step of wiping and setting it up as a new device, then downloading apps back on to it. I also had to use some convoluted steps to restore some data to apps.
That was about a week ago and afterwards battery life was excellent - after several hours it was still on 100%. By the end of the day, it was 70%. A week later though and it has suddenly returned to being terrible and running warm in my pocket. This morning I did a hard reset (home and lock buttons until reboots) and the used the multi-tasking toolbar to kill off every single running application incl. the built-in Mail, Phone, Contacts etc.. until nothing was left. I think I've turned off Safari iCloud syncing too temporarily to see how that affects things.
Since then battery life has returned to being good but I suspect there's some issue of conflict between some apps and the updates to the iOS, or that there's a memory management bug somewhere that takes a while to manifest. It maybe that your upgrade to 6.1.4 has temporarily done the same reset for your device and the problems will start to reappear after a week or so. For reference the only apps that I have run today (and therefore show in the multi-tasking toolbar), seemingly without problem, are:
Notes (iCloud synced)
App Store
LED
Remote
Phone
Mail
Settings
Photos
eBay
Facebook
Pages