Tim,
That's a tough one - some great suggestions have been made above but I think you will find that the solution will lie somewhere in what you originally suggested - fairing the boards or reshaping the trailing edge. I can't speak from experience because I struggled to get my 6.0NA to be quiet (my 5.2 sang loudly too - but I never tried to fix it). I reshaped the trailing edge of the boards to no avail. After consultation with a lot of different people, my next task was going to be to look for "hollows" in the profile of the board and fix those if any existed. The way it was explained to me: take a straight edge and place it along the board (or rudder) vertically. Look for hollow spots as you slide the straight edge fore and aft. These concavities - particularly if they are uneven, apparently can cause the singing. Try filling those up maybe?