Ahem, I feel a bit stupid posting this. Please don't laugh too hard.
Thing is, my wife had a dream last night (no kidding!) about me attending an AGoT tourney. In the dream, they had a rule that each participant had to bing six decks, one for each house, and the deck each player had to play each round was chosen randomly.
Now, I actually think this would be a fun idea. There would be some practical problems, obviously, such as the fact that you'd need many copies of some staple cards. But that could be solved, I guess. You could allow players to switch in the necessary plots or neutral cards in between rounds. Or, a more radical idea, you could only allow each card once per card title, over all six decks, to encourage diversity in deckbuilding. What does everybody else think?