Rough sketch of a potential process: Harley Q. is riding through the hills with the throttle open when her phone buzzes, indicating she's approaching an area with residents willing to pay above her threshold for <80db experienced noise. She rolls off the throttle and coasts through the upcoming neighborhood, or takes the long way around. Maybe a small extra payment would be put in escrow if she doesn't approach that area while making noise for a few more weeks.
Please note that the apparent bias toward paying the noisemaker is an artifact of existing noise ordinances. Coase can only help us from where we currently are, not from an imaginary utopia.
If we place this in a hypothetical city with a 40db noise restriction, which allows neighborhoods to accept louder noises by consensus, the payments reverse; Ms. Q will try to select the cheapest neighborhood she can enjoy her noise through, and its residents will end up collectively richer in exchange for suffering through the noise.
It's not at all like that, because punching people is currently illegal, and making noise up to a certain threshold is legal. I like peace and quiet more than I like making noise, so I wouldn't mind a lower legal threshold; but the advantage of paying people instead of fighting to change laws is that there's no actual fight.
The advantage of casting things as a moral struggle instead of a difference in preferences is, of course, that you might be able to gather enough allies to defeat the other side and take their stuff.
If you do have the ability to reliably get laws changed at some expense, you should bring that up while bargaining; it will give you a stronger position. You should be able to get a deal that's better than actually spending whatever resource it would take to change the law.
This is an interesting perspective. Can I ask what your background is that exposed you to this way of thinking?