We have coaches. Why not referees?
Give rewards to people who participate as referees in the same way that you do coaches. If somebody is griefing in game have the option to request a ref. Ref shows up and can analyze chat logs and behavior and potentially inact immediate penalties to the person who is ruining games.
All in all I think the immediacy of this approach would be more motivating for griefers to stop than a potential ban on the future that may or may not happen.
Refs don’t have to show up at the very beginning but can if necessary. You can respond to referee requests in the game client when a player or team requests one like coaching. I’m sure this idea could be expanded and refined but I think having a real person their or even just the potential of a real person showing up would sway a lot of griefers from ruining games. Let me know if you have any other ideas that could be added.