I've been to several large and extensively competitive games over the years. Honestly, if you need an over abundance of refs then there is a problem with your player base. I personally am a fan of having lots of "in game" admins though; kind of like secret shoppers.
Players/teams that cheat usually do so because it's in their nature. I would just remove or ban individuals that cause issues to set the example. If someone is calling their hits and playing sportsmanlike only because someone is looking over their shoulder, I wouldn't want them out there.
Just my thoughts. Your game idea sounds fun though.
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