> something new, that lets you talk with people you actually know.
Anonymous Facebook? The problem with that is this:
> so places like Twitter end up filled with unreasonable narcissists
That's also a problem among the people you know and have added on Facebook, many of them are unreasonable narcissists and they don't mind showing that with their name and picture on the web. I feel like giving them anonymity can only make things worse. Just think of your racist uncle, your Nazi grandparent, your homophobic friend, but now you won't know which of them is posting the bullshit.
You have chosen a very difficult problem to solve, I can only tell you why I think your current idea won't work and wish you luck.