Instructions for clean restore and then getting your contacts, at least, back? Simple as restore on the phone's settings?
Forgive me, here you go:
1) Plug your phone into your computer and open up iTunes
2) In the top right section of the window there are two options: a) Check for update and b) Restore iPhone. Click on "Restore iPhone"
3) Follow the prompts. iTunes will download a "blank slate" iOS 7 file, and restore your phone with it.
4) After installation, the phone or iTunes will give you the option to "Set up as a new iPhone" or "Restore from backup". Do not restore from backup.
5) As long as your contacts/calenders/mail is backed up to iCloud, they will all come back after you sign back in to iCloud. No restoring from backup is necessary.
Instead of restoring from backup, set up the apps/music/settings as you want them. This will take some time but is way worth it.
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Everyone always says this but I've restored from back-up since my 3G and never had the battery issues. I just check all the settings when a new iOS is installed and make sure anything likely to be an issue is turned off.
I always do a couple of full cycles too - drain battery to 0 and charge to full, I'm not sure how clever battery management is in these devices but perhaps a new iOS needs to "learn" how much battery you have so a fresh install will naturally run down quicker until this is done? I could well be wrong
I agree that Apple should figure out the drain issues that occur from restoring from backup. You should try a clean install. Backup your phone first, so you can go back to the backup if you want. But I bet you'll be pleasantly surprised at the performance/battery life if you don't restore from backup.