I hear you on the needlessly confusing iTunes restore, synch procedures. For sure before I ever do any of them I backup the phone so I can get back to where I was if something screws up.
Mine was a brand new phone so I wasn't worried about losing any data so just did restore thru iTunes, but maybe Settings>General>Reset >Reset All Settings would get rid of whatever is causing the miscommunication with Update. That will set the OS back to factory defaults but it won't delete content, just settings, passwords, etc. there's a discussion of how, after doing Reset All, to Set Up Like New Phone here:
https://discussions.apple.com/thread/3859841?start=0&tstart=0
Make sure you don't hit Erase All Content and Settings cuz that WILL wipe your phone. Tho even that should not be a problem if you backup immediately before trying any of this. I'm assuming you back up to a computer via iTunes.
Can't comment about iCloud backups yet. I'm still trying to figure out how exactly the iCloud works as I have pics on my iPad that came from my old phone via iCloud but don't show on my new phone.