The tribunal is a great idea, peer judgement is a win win for all sides.
However I think it would be a great idea to create a mobile app for smart phones. I believe that you will see ally more participation.
My personal example:
I run the tribunal if the servers are down, I don't have time for a game, or I'm waiting for a friend to finish. Otherwise I'm feeding the addiction and perfecting those last hit tactics with a new champion (Kog'Maw is my current project).
Give me a mobile app and I will get to smite those who deserve smiting on my free time away from the computer.