How about this idea...
It's clear that you are an individual that appreciates fair play on the field and wants it to be recognized. The manner you want it to be recognized in has a couple of faults, so be an innovator for your team.
Make a team Fair Play award. You can make a certificate, or a mounted poofy ball, or something similar, to a team you think plays the game well and gets the job done right.
If it's recognition you are looking for, that will give you quite the image - of caring enough to honor teams that you may be against for the entirety of elimination rounds, or teams that you never play against, or teams that aren't selected for the finals but clearly did something right.
I like how Jack Jones put it - the referees enforce the rules. Be your own judge and follow the rules. You shouldn't need an award to do it
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