Eliminate the instigator fighting minor and go with new instigator rule: making the instigator fighting a major penalty goes along with game misconduct. The person that defend the fighting will not be given game misconduct and will not be given a penalty for defending himself with one catch, the hit has to be extremely clean. If it is clean but you fought, you are ejected from the game to the player that started the fighting. The player that made a clean hit will not be ejected.
This will reduce senseless fighting after a clean hit and any dirty hits will be now allowed for fighting and not being given a game misconduct upon a review. If the hit is clean upon the review and someone fighting him, will be given a major penalty via the instigator fighting. Any dirty hit is now reviewable after the fact with the risk if the review showed a clean hit will not be given a major to the person who started the fighting after the fact. No more 3 minute major PP when someone instigate the fighting even if he deserved it. It will remain a 5 minute major even after the fighting one way or other. You want to encourage a huge hit for as long as it's clean without dragging down and resort the fighting. Even if the ref missed it, any fighting is an automatic review if anything happened behind the play that the ref missed and the coach or the captain has to point it out that they saw that the ref missed for the fighting to be justified. Ref now no longer be blind to any missed call and force their hand to the ref with the review.
No more mutual fighting and any mutual fighting will deserve a game misconduct and an automatic one-game suspension for both combatant.
The ref will have to ask, is there any reason for fighting, and if one of them said no, it is for show, still get an automatic game misconduct and a game suspension. If one of them said, it came from the last game that someone did happened will still get game misconduct and a game suspension. If someone said, he crossed checked and got hurt is the main reason then the ref will review it and determine that if it is justified fighting, and if not, he get a major instigator penalty and a game misconduct and the other combatant will not get any penalty and stay on the bench. If the fighting is justified, the person who cross-checked will get a penalty and the person who fought will not get a penalty. That is how you police the game forcing the ref to review. The only exemption is tripping, hooking, or even holding is not the reason to fight.
When you instigate the fighting that will not result in any fighting major that is justified, it has to be one of those penalty: boarding, cross-checking, high-sticking on purpose, spearing, charging, elbowing, kneeing, slew-footing, and goaltender interference, or even any kind of interference that resulted in any injury major type of penalty where instigator fighting will not be applied to any player that defend themselves.
That is what I would do if I were a commissioner for a day, you are sending a message that any type of dirty antics will not be tolerated that interrupt the game and it is okay for you to police the game if you felt that ref missed the call but do it so with a risk, if it is clean, you risk getting kicked out of the game for nothing.