[Short version] The iTunes backup for my iPhone 6 Plus would not restore to my brand new replacement 6 Plus. (The error message was that the backup was corrupted or incompatible with the device.) I purchased iBackupBot. I had trouble doing a full restore on it, so I decided to try each component separately. It appeared everything restored OK except for my text messages. There was a note when I tried to restore them that I may have to do a "full restore" and check "Remove items from device that will not be restored." I did this, and all seems to have gone well. Except, my contacts are now pulling from a much older contacts database (from Feb 2012 - maybe an old icloud database?).
In iBackupBot, under User Information Manager," I can see ALL of my current contacts, but when I restore, it only populates the Feb 2012 version. I have tried to restore from that User Information Manager tab, as well as a "partial restore" from the backup, but I still end up with that old version of contacts. My icloud "contacts" is off. Maybe there's a way to export the contacts I can see, put them in a usable file, and re-import them?