Sounds good in theory! Unfortunately, life does not always seem to fit so neatly within our postulates. For an example, a man is running at your young child with a cleaver in his hand and is screaming that he is going to kill that devil. How do you translate your theory in practice in that moment?
Speaking for myself of course, the simple answer is "the best I can." Maybe another way of looking at this in terms of absolutely peaceful efforts would be to change the situation to having one loved family member chasing after another with the cleaver. Or let's begin with an operating assumption that the attacker ingested something accidentally or is otherwise acting in a way that might be described as accidental.
The question then becomes one of means and ability. A lack of peace-based effort might induce us to simply blast that person when we might have just knocked him out or otherwise eluded him.
If someone were to try and kill my child I would easily want to defend my child and not so easily want to protect the attacker. This is pretty natural, and I think demonstrates a natural hierarchy of importance, but this is where the focused effort to be more peaceful comes in (i.e. training to be successful at peaceful behavior). Where possible (and recognized as such) acting with peace in mind means providing an opportunity for the attacker to learn from his mistakes.
To my mind the practical side of this comes from the tendancy for people to listen to those they relate to; people who have been in similar situations. If I'm trying to convince a violent aggressive person to stop that behavior, I'm going to have less credibility than someone who also exhibited that behavior, but later chose more peaceful efforts. That's the "why" for me that justifies peaceful efforts in the light of extreme violence.