A single, seeded medal round as the second stage
I ran several round robin/Swiss tournaments during my event. It worked really, really well. The participants, though, like to have a game that decides everything, so at the end of the round robin or Swiss, I ran what we called a "medal round." The first place from the round robin/Swiss played second place for the gold medal. Third played fourth for the bronze. 5th played 6th, and so on. The displayed 1st/2nd/3rd did not always match the actual results because of this medal round.
I see two ways of accommodating this. First, allow the ability to manually set the final standings, despite what the results seem to say.
Second, this could be automatically set using the second stage of a 2-stage tournament - the option for a one-round set of matches that decide the results. The matches would have to be designated as to which place they are playing for (1st, 3rd, 5th, etc.)