1: Make the tie breaker related to playing position first and then go to investigators. So, if you played 3 rounds in a two player game then the person who had to go first twice would win because they were at the disadvantage of going first. If it were a five player game, then each round would give a bonus of some amount decreasing to the first four players each round. So MAYBE first player is allocated 4 tie breaker points, then 2nd gets 3, 3rd gets 2, and fourth gets 1. Fifth gets 0 for the benefit of going last. And these only apply if a tie occurs at the end and the game calculates which of the winning players has more tie breaker points. If still tied then go to investigators.
2: I would like to either be able to choose the number of rounds played in a game or force 2 player to be 2 or 4 rounds. It eliminates the issue completely about who has to go first 2 times while the other only goes once. I feel this would be very beneficial in tournaments especially. Going first in a 2 player tournament sucks because you are at an immediate disadvantage.