I have a little bit of experience as a chess TD. Here is how I would do it.
* Games are two-player. With big prize money on the line, 3+p will be fraught with opportunities for kingmaking and collusion, and the integrity of the tournament would be difficult to maintain.
* Until the semifinals, matches are best 2 of 3. Loser plays first. The winner of a coin flip of each match chooses: play first in the first game (before seeing the Kingdom cards) or win the tie if the match goes 1-1-1 (or, by some crazy chance, 0-0-3). (I would prefer another game, but this is my concession to limited time.) In the semifinals, matches are best 3 of 5.
* The tournament structure is double elimination. With 256 players, this will produce a winner in 9 rounds. It allows all players at least two matches, and there is no incentive at any point to throw a match.
* If an independent Dominion system is available (Iso, Goko, whatever) that system is used to determine seeding. Otherwise it is random.
* Time is 75 minutes per 3-game match, 125 minutes per 5-game match. This allows a little bit of slack time.
* Players are required to play briskly. At the 45-minute mark, if game 2 is not finished, a TD may observe the game. If one player is playing slowly, and the match times out, the game will be adjudicated in favor of the opponent. Blatant stalling in the judgment of the TD will result in a disqualification. If both players are playing slowly, and the match times out, the third game is marked as a draw, but if the match is 1-1, the winner is decided by coin flip, not the tiebreak mentioned earlier.
* Depending on the tournament, Kingdom cards may be selected either randomly or at the discretion of a celebrity set designer--i.e. DXV or his chosen heir. A randomly chosen Kingdom is mulliganed if there are not at least two cards costing $5, per DXV's statements about what makes a good Kingdom. They will not be revealed before the start of the tournament in any event. The Kingdom cards change each game, but during each round of the tournament, each set of players plays with the same Kingdom cards. This allows commentators to compare different strategies post-mortem.
* If random Kingdoms are used, players may opt to use veto mode. Veto mode is a tournament-long decision, and a match is played in veto mode only if both players have opted for it. In veto mode, 12 Kingdom cards are chosen and each player, in player order, chooses a card to eliminate. (I considered having the choice be made before the players know who is going first; but this prevents us from having the who-goes-first choice made before the Kingdom is revealed.)
* There is no identical-starting-hands rule.