... solution to violence ...
I think you are looking at this the wrong way.
Your goal is less violence as an end in itself. When violence is a means towards any given end. Maximum total material wealth turns out to be produced by using violence only in defense of private property.
Violence is simply a feature of our physical existence and isn't going anywhere.
I don't disagree that violence is suboptimal... which is why the optimal use of violence is violence against violence. But of course violence is poorly defined, private property for instance - is stealing violence?
You could punish stealing only by stealing back more (without real violence). Debtors prisons are gone for example. Fraud could be punished by black listing like bad credit is.
But if you have someone that is going to slaughter and eat everyone (which can go on indefinitely, suboptimal or not)... what else are you going to do but violence back.