The best way for this to work is to not have the author involved at all, or only to give permission to use the fic. That way the stories can be seriously discussed as literature without the pressure of only being able to make positive remarks.

The library book club I once belonged to used published fiction with no author present. I don't like the "Oprah" model where the author is right there listening to every word. No wonder all comments were always blandly positive.

I agree that comments shouldn't be downright nasty, but we should feel comfortable questioning motive and character development within the story.