How about to implement a cross-board reference support? It can make a huge shift towards the justification of tension between competing boards.
For example, if we have a board with schizo moderation, name it board1 and its competing board with free posting, named board2, then a user gets banned on board1 for nothing, and so one can not dispute the ban, but still can post on board2, and then he/she posts a reply to board1 post in board2 thread, referenced as >>/board1/post_id and then this is reflected in board1 post xrefs. Then, interesting outcomes can follow. For example, people from board1 can see there is a reply link on another board. And a moderator of board2 has no options to ban this reply from being shown in reply's list, so there is a next dramatic dilemma for schizo moderator - to ban a poster, who is replied to, or just to 'OK' with it and see people leaving to board2 where the freedom of speech persists. This can bring a huge balancing effect.