It does persist after power down and restart. I haven't reset the phone yet as I am trying to preserve the contacts and photos for my mother. I was able to get into safe mode following the directions you linked B. Diddy.
With the screen on, press and hold the Power key. (Pass)
In the options menu that displays, press and hold Power off. (Pass)
Restart in Safe mode' displays, tap OK to restart in Safe mode. (Pass)
Upon restart, device displays 'Safe mode' at bottom of screen. (Pass)
The error continues even in safe mode, and com.android.message popped up once as well.
Sounds like you installed a App through APK that's not compatible.
She shouldn't have been able to as i never enabled developer mode and she only gets apps out of google Play. She did recently install a new puzzle app, Woody.