Again, I'm not an expert in information security by any stretch, but perhaps you could just encourage your users to use LastPass or Keeper to generate and store large (truly) random passwords for them, and store them in the secure vault? And to use 2-factor authentication too.
I realize LastPass was recently hacked, but users that chose long, secure LastPass passwords should still be safe from having their vault opened. Users that chose a weak password as their master password can't be helped anyways.
Of course, its not the best plan, but it should at least put your users on the right track. There is alot of inconsistency in security between websites, I understand that (for example, my bank allows a maximum password length of 16 characters, but my reddit password is 100 characters). But 16 random characters is still better than having to write down the password because you can't remember it.