The rewards could be: Ship skins. Bridge interiors. Trophies to hang on your ready room wall. (Please, no overpowered in-game items for rewards, the real reward should be the admiration of your peers.)
The focus would be team play, not individual prowess. Both PuG's and Premades would be able to participate in separate ladders, coming together in a final playoff match only.
Players register their ship and captain with preferred playtimes, (no revolving ships in PuG's)
Premades register 7 team members to allow replacement or rotation of members and ships to suit the battle they anticipate.
The first ladder is assembled aligning players, (or teams,) of similar preferred playtimes to match up and a schedule created to limit the first round to a 24 hour period, so a time limit of 10 minute matches may be required in the first round if 14400 players register, or more likely an hour per match in a more realistic turnout.
For PuG's, the published time will allow them to schedule play and meet with teammates for strategy sessions, while for teams it would allow them to tailor their final team and ship composition to face their specific foes.
'Extra' players who cannot be fitted into a team can fill in as replacements if a team shows up short a player.
Players on the losing team are eliminated, and for PuG's, the winning team players are again randomly assigned to teams based on preferred playtimes where possible. In this round players who were unassigned replacements in round 1 will be included in the selection and 'extras' will again be on standby for replacement.
For Premades the same applies, but they may freely choose from among their seven players for entry to the next round and need not specify which of their seven will play until start time.
Same as Round 2, but with half as many players each time.
Assume 100 teams, (500 players, which is way beyond my projected likely turnout,) the day would consist of 50 20 minute matches, with winners advancing to the next round.
The second day of the tournament would consist of 24 matches which could be up to an hour long with five players either replacing absent players or playing against un-slotted players from the first round for a 25'th round.
The third day would consist of 12 matches of potentially up to 2 hours with five players on standby or matched against un-slotted players from the second day.
The fourth day would be finals day, with six matches, then 2, then 2, with the players taking the bye determined randomly. Then a final battle between the winning PuG and the winning Team would be held.
I would assume a three day tournament would be sufficient for the numbers of players available and interested, but the stir this would create as players post their battles to the various video sites would do a great deal to promote PvP. This would also generate a new level of bragging rights, especially if wall trophies came with a description of the event in which they were earned.
I would like to emphasize the way this idea is structured, it would emphasize team play. No matter how good you are, if your team fails to advance, you fail to advance. You would be required to communicate with your team and to heal, give fire support, and otherwise work as a team to make it to the final rounds, even though each round will find you grouped with four other players. It is my belief that by the final round, the PuG's will be every bit as good as the team they face, but the truth is in the testing.
This idea could also be applied to ground PvP. I recommend a new tournament every three months, alternating between space and ground combat, with hype to build up to it, and promotion of the event as both a recruiting event for PvP players and a recruiting event for STO. More players in PvP means more players!