If you've tried everything else, a factory reset is the next step. I agree that it's also a bit of a last resort, but Google's retore options are a lot better than they used to be.
The first thing it to make sure that all your online data (emails, calendar etc) are synchronised. Then back up any content (photos, music etc). An SD card is the easiest way to do this if you're not using one already. Remove the card before you reset as the process sometimes formats them.
Check that the deevice itself is fully backed up. Backups are viewable in Google Drive and you can see the date. Recent versions of Android have a Backup Now option in Backup & Restore in the main settings menu.
When you sign in again, choose Restore from the same device and all your apps and quite a lot of your settings will come back automatically. You'll probably lose data from 3rd party apps, though you can see which ones back up to Google within the backup itself and some may also have their own export or online backup options.
You'll still have to set up your homescreens again and screenshots before you start can help here (remember to back those up too!). It's also worth checking that any apps (eg news) you told not to use mobile data still don't and that Google Play doesn't update over mobile data unless you're happy with that.
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