The problem with round robin tournaments is that they can produce a situation where there is no clear victor, especially when the amount of games is so few. It's quite feasible that over the course of the 3 games that would decide a 3 team round robin tournament (Where the teams only played each other once) that 1st and 2nd place could end up being completely evenly matched. How would you separate them then? Do we really want a situation like what happened in England's group at the 1990 world cup where
2nd and 3rd place was decided by drawing the team name out of a hat?
A knockout format is best, but we want the odds to be stacked in favour of the team that finished higher up the table. I think also that any one team should have to play a maximum of 3 games.
I'll tweak my earlier suggestion as it gave no benefit to the team that finished 5th over the team that finished 6th.
So 6th place should play 5th place at 5th's home ground, the winner of that game should then play 4th at 4th's home ground, and the winners of that match play 3rd place at Wembley. Ideally the final would be played at the 3rd teams home ground, but the powers that be would never agree to that.
This gives every team an incentive to finish as high up the table as possible. By playing the games at one of the teams home ground it also solves some logistical issues as the tickets can go on sale earlier, as all the dates and locations are known.