I've seen Dad run this scenario for 6+ new players a few times, but he is quite familiar with the rules.
Having an umpire will be a great help! Here are some suggestions that might help as well....
1. Limit the size of the leagues. Maybe even cut it down to 1 Leader, 1 Sidekick, and 1 Ally per player.
2. Add an extra minor plot point.
3. As the ump, focus on who currently controls the Initiative and encourage them to keep the action going.
4. Stress the fact that this is a "learning scenario". New players tend to focus on the fighting far more than completing plot points, so don't worry if this happens and just let them have fun.
5. With 6+ players there's a chance that you'll draw all the Fortune cards, so just be ready to shuffle as needed. Also, new players tend to ignore their cards.
6. The League Deployment in this scenario is perfect for big games but you probably want to expand the table to 4'x4' - but not more than 4'x5'.
7. Have lots of fun!