Creating public profiles on private site

As expected, anonymous members cannot see the profiles of authenticated members on my Commons site (eg, user/5/about).

However, I would like to give authenticated members the option of marking their profiles as "public" and allowing anonymous users to view those profiles.

It is easy to create a view for a user directory of public authenticated users. I'm not sure how to clone the user/#/about pages to create a version for public profiles. What is it that I would be cloning or copying? Would I add a context to handle public vs private?

Also, ideally, I would want a url such as user/public/first name-last name/about. Would I go about this in URL aliases, and what would I be making an alias of (I suppose this has to do with the answer to my question above).

Thanks for any help.