So following this quote right here:
What would actually happen if I formatted Emunand in System Settings? Is it possible to unlink/re-link it from here?
Nor do you have to completely delete your NNID.
You just have to make an emunand backup and a backup of your nand's folder in sdmc:/Nintendo 3DS/, then format emunand in system settings, re-link your NNID in your newly formatted emunand, then restore emunand backup and restore your folder in Nintendo 3DS so you don't lose your games and your saves.
Voilà, should work now.
What would actually happen if I formatted Emunand in System Settings? Is it possible to unlink/re-link it from here?