You hit on a very crucial point here. That of God's justice. I am hoping to dig into the "behind the scenes" necessity of Christ's atonement.
It is amazing when I look into the different "isms" that arose over the course of the church's history, to discover how today's beliefs on many things, but also the atonement have gathered bits and pieces from many of them, and come up with a conglomeration that cannot even be classified into a single "ism" or this history, and has a multitude of branches. From Pelagianism to semi- Pelagianism; Socinianism to Arminianism; Progressive to Open Theology. All these things contain points of disagreement with one another, and yet we have teachings as seen on the forum that would deny all of them and yet retain this from that, and another thing from over there,and have no idea they are doing so.
Oddly the only thing that remains relatively consistent is Calvinism, unless you count the new Calvinism which I know nothing about.
These views, all at one time or another found in any of the "isms' mentioned above (excluding Calvinism) have a variation of a misconception of the atonement (because it is scripturally unfounded) of the four things found in the OP.
So let's start with the misconception of sin. Nearly all of the above deny original and imputed sin. Arminius did not, but believed that in the atonement Christ made enough grace available to all men without exception to overcome original sin and choose Christ.
Sin renders us guilty and binds us over to punishment. It is spoken of as a debt which we are bound to pay to God's justice.(Col 2:13-15) Through sin, God becomes our enemy and we hate our enemy. This of course is a crime against our Governor, our Creator, our King and we become deserving of everlasting death. Therefore we are called debtors (Matt6:12), enemies of God, actively and passively (Col.1:21) guilty before God.(Romans 3:19)
Therefore, in order for us to be redeemed (which always infers a debt paid by one in the stead of the debtor) the payment due because of our sin must be made, thus appeasing the divine wrath and the expiation of the guilt.