I did a full disk backup last night, and then did a Restore on my iPhone 5. The process reinstalled my firmware and iOS 6.02. Immediately my Verizon "Invalid SIM" problem and my iOS 6.02 update battery drain issues went away, and for the first time ever I can sync to iTunes wirelessly. I feel like I have a brand new phone. I don't recommend this for everyone, because you still have to re-upload your music library and various other things that aren't part of the backup, but if you're having any of the same problems I was, go for it!