Nevermind, I just figured it out!
In the “hidden” input types, I just replaced $comment_author with $user_nickname and it works fine.
I am interested in this as well – I have installed the hack to only allow registered users to post, and wish for it to automatically transfer the information from get_currentuserinfo() to the posted comment. I tried using the above code posted by friend_of_grommet, but it still posts the comment from Anonymous. Any further advice on this subject?