I have now played in two official tournaments for AGOT (gencon), so with that substantial background I feel I am able to comment on what exactly needs to be done.
Melee:
* Officially announce that seats are to be randomized. I am not sure even what is the most advantageous way to sit, but there is no reason to not to do this.
* All rounds should be seated swiss style. It works for joust for a reason, and will work for melee for the same reasons.
* Ties should be broken if one player did not get to his challenges phase on the final turn (assuming someone finished the game)
Joust:
* 5 points for a win, 2 points for a Draw - players can officially decide the outcome of a match without playing. This is important because I felt that people were unfairly hurt by the timing out rule if the judge happened to be watching their game. Also the losing playing should never be put in the position to have to decide if they 'give' a full win or timed win. It's terrible to be put in the "should i be a jerk or be cool" position
* Tiebreakers should be decided by opponents win percentage, not opponents total points...and there should be a floor (.25 or .33) to how bad one person can affect your score. This solves two big problems 1)winning a regional gives you an arbitrary 5-1 bye which is massive; and 2) people dropping totally screw their opponents schedule and at gencon I assume a fair amount of people drop because there are a million things to go do (as opposed to say a regional)
As a note. I was initially frustrated at ktom for enforcing the timed win rules. But it's quite clear the rules give you the timed win unless you win in time. There is nothing in the rules that allow you to give your opponent the full win. It's not his fault that the standard way people behave goes against the rules.