On the other end of the spectrum, I would be happy if I could install a wiki and share the login credentials between WordPress and the wiki. I hacked MediaWiki a while ago to share logins with another site (in ASP Classic) via session cookies, and it was a pain to do and even worse to maintain. Ideally, I would like to find a plug-in or someone who knows a more elegant solution.
The tutorial WordPress, bbPress & MediaWiki should get you on the right track to integrating MediaWiki into your WordPress install. It's certainly going to be a lot easier than hacking WordPress to have wiki features, especially with the sort of granular permissions you're describing.
Another solution is described in The CUNY Academic Commons Announces WPMu-MediaWiki Single Sign-on. It just creates something that uses the WordPress login as the master.