In my opinion the wet balsa has got to go if it's really wet and starting to rot (it's rotten when it dark brown/black and smells). The rudder is just going to flex and further the problem. If it's wet and the balsa is still white and structurally strong than dry it out like kooslouw did and you should be fine. If the balsa is dry then drill out the holes for the hardware and fill the holes with epoxy/collidical silca, cure and redrill.
Anyone have any other thoughts?