Why not have a sub-heading next to 'All Activity', 'Questions' and 'Unanswered' that redirects you to a list of questions without a BA making it easier for Mods to do BA sprees and giving users the chance to put forward an answer for questions in which their are not many votes/answers.
I got BA recently on a question in which no answers had more than 0 votes for a question that was asked on February 2011. I have no up-votes because no-one really goes on old posts but my answer got BA and the other answers (most had negative votes) were removed/hidden.