I fixed my iphone a couple of weeks ago and posted about it here.
I think the answer might be to completely wipe and reinstall from backup Twice.
There could be a persistence of memory/ settings just doing it once.
As we can't remove the battery we have to be sure that the phone has lost its rogue processes.
When I did it (iphone 4) I first backed up via iTunes and did a reinstall as a new phone.
I thought it would be OK to start again and put all the things back in but it was too much like hard work so I shut down and then did a wipe phone again. This time I opted for restore from Backup and let iTunes do it's thing.
When it had completed the phone was running perfectly again.
I'd inadvertently run it twice, that's the only part that's different to what others are doing.
Just keep wiping and reinstalling until it gets the message!