re: Is there a way to display the Public/Private options in the Entry Form when a User is not logged in?
Sorry, no, for a user to see those options, they must be logged in.
re: I have the directory set to public override so that private information can only be viewed by members who log-in, but the general public can see everything else.
From what I read so far… I suggest disabling this option as it is not needed under normal usage.
Hope that helps!