I came from another multiplayer card game, Vampire: The Eternal Struggle. That game is exclusively multiplayer, with 5 player tables being best and 4 player tables acceptable when the number of players is not divisible by 5. The game just doesn't work 1v1.
Most often a tournament is played in 3 preliminary rounds with one final table of 5 players. The best scores determine the final table. Originally your score was only the number of players you ousted (defeated) and also one additional point if you were last man standing. If you swept the table you got 5 victory points (VP) that round. Since it is a multiplayer game (and even some of the game mechanics, like voting almost require it) deals are to be expected. However, some players would make deals to divide up the victory points by saying I'll help you win (get 3 VPs) if you help me oust my prey (1 VP) and let me withdraw (a way to leave the game "alive" for 1 VP). If the tournament didn't consist of a large number of players you could comfortably get the finals by taking 2 VPs each round and never winning a table. Sometimes this table splitting got so bad that players started doing it in the first couple turns or even on turn one. To combat this, a new point measure was added, the Table Win (TW). Each 5 (or 4) player table would only have 1 TW, and you had to earn at least 2 VPs and more than anyone else at the table (5-0-0-0-0, 4-1-0-0, 3-2-0-0-0, 2-1-1-1-0 for example) to get the TW. Table Wins were the first consideration in making the finals, so now the player that had 1 TW and 3 VPs placed higher than someone would traded VPs but never won a table with 0 TW and 6 VPs.
This really helped and also led to another rule, Play to Win. If you had a reasonable chance of winning a table a judge could forbid you from taking a bad play that would hand the table to someone else. This was to fight collusion. In round 3 if you already had 2 TW you were probably guaranteed a spot in the finals in all but the largest tournaments and could try to throw your last table to a friend (you didn't "need" the TW). With Play to Win you had to try and get that TW if possible. Once there was no longer a reasonable chance of getting the TW you were to try and maximize your VPs. So there was still the opportunity to make a deal for VPs once you couldn't win, but colluding undetected was very difficult.
Finally a rule for just the final table was added late in the life of the game. One player wins, all other finalists tie for second. This eliminated the situation where two players have a chance at winning and a third player can become kingmaker by making a deal for second place. With only one winner, there is no reason to deal for VPs because you still tie for second if you don't win.
I think the Table Win concept could be easily applied to Melee. I don't know if it would have made a difference to the top 16, but my guess is that someone went 1st, 4th, 4th and missed the cut to someone that went 2nd, 2nd, 2nd because they sold first place each round. On both my second and third round I had players trying to deal for second place, but doing it the other way. Someone with a strong shot at first tried to convince someone to hand them the game by offering second place. Maybe its just me, but I'd rather see the leader get ganged up on by the table then see someone get bribed to end the round early by giving away first in exchange for being boosted to second.
I was fortunate enough to make the top 16 and I really appreciated that only first place advanced to the finals. Nobody cared about second place at that table because it meant the same as fourth, you're done.
I don't know if final table is 1 first and 3 tied for second, but I don't think it would hurt. One problem might be the reward for winning. Designing a card is something you can share with your friends, so the prize itself is an incentive to boost your friend if you cannot win on your own.
I hope something can be worked out, because I really like playing Melee with my friends and would like to enjoy playing it in tournament.