The solution posted by IKevIKev
is the method that we used and it works well. This is to be considered an addition to that solution.
We worked in a pattern where the person creating the match always went on to win. This allowed the next winner to create the next match and have it ready so saving a bit of time.
It does take a while, but we all wanted it and worked as a team.
I would add that you can also save a bit of time by avoiding any 2nd round matches.
If the overall winner waits an extra 20-30 seconds before advancing from the 1st round match, it allows time for the winner of the other 1st round match to quit out.
This prevents that person getting pulled into the 2nd round match of the tournament and therefore saving some time.
The reason you can get pulled into 2nd round matches is that you will find that 1 person will quit out before the other and it then takes a bit longer for the remaining person to exit the game.
If the overall winner is a bit eager on forcing thru to the next round the other 1st round winner will not have time to get back to the review screen and quit out.
When you have 200 matches to do between the 4 of you, saving this small bit of time will add up over all the matches.
We got into a good flow after about a dozen or so matches and only occassionally slipped up, mainly as not all of us were on mic in the party.
Once you get into the flow of things it's easy enough, and the overall winner started to use the rotation of the table to judge when to continue.
I understand it's not a full solution and maybe it should have been added as a comment, but as this is my first, I'm hopeful some will find it handy and it's OK.