I don't think that you and I are talking about "justice" in the same way, and as as result we aren't talking about the same sort of justice.
My sense - and I don't mean to put words in your mouth here, I'm just advising you what I'm getting from your post - is that your sense of justice is what lawyers do, in that they see competing interests and try to work out an arrangement that keeps some semblance of civil peace by having both parties to a dispute recognize that the other has some degree of merit (more or less, depending on the underlying evidence) and adjust remedies accordingly. (If I'm wrong on this, my apologies . . . but that's what I'm getting from your post.)
That's not what "justice" is when scripture is using that term, in my view. "Justice" has more to do with what God expects of us in our relationships with each other, probably interpreted best in accordance with the Great Commandment (which for me has recently become to be relatively synonymous with the concept of cognitive empathy that iuwclurker has mentioned elsewhere on the board and a related concept of compassionate empathy, which is different from emotional empathy). For some good reading in that vein I suggest Kierkegaard's treatment of "as yourself" in his
Works of Love). And the application of "justice" is primarily associated in scripture with not exploiting other people . . . economically, financially, sexually and every other way you can think of.
To arrive at this type of justice is like focusing a camera through two lenses, not one, with one lens being a worldly lens - what makes sense on the relative merits of the evidence, much like I suspect you were describing - and the the other lens being through God's perspective on things.
By the way, the public figure who most unabashedly put theology (as opposed to mere religion) into presidential policy was Abraham Lincoln, according to a fascinating book by Elton Trueblood (former president of Earlham College) I am currently reading. Trueblood quotes Reinhold Niebuhr's observations regarding Lincoln's exercise constant vigilance with respect to this dual lens approach to decision-making:
"This combination of moral resoluteness about the immediate issues with religious awareness of another dimension of meaning and judgment must be regarded as almost a perfect model of the difficult but not impossible task of remaining loyal and responsible toward the moral treasures of a free civilization on the one hand while yet having some religious vantage point over the struggle."
Trueblood's overall thesis is that Lincoln's greatness as a president derived not only from his brilliance as a politician, but also because Lincoln took the extra step of working toward policies and actions that he was convinced were in concert with God's will. For a good window into this aspect of Lincoln, you might read his Meditation on Divine Will (
http://www.abrahamlincolnonline.org/lincoln/speeches/meditat.htm), which according to Trueblood was the basis for Lincoln's resolution of the larger issue regarding slavery, which took him from a position of compromise and into an insistence on both saving the Union and ending slavery in all US states.