Satisfaction isn't about making people miserable.
That people can be and often are happy in the midst of suffering, I admit; that suffering isn't itself misery, I deny. It is the very definition of the word.
It's not Christ's misery on the Cross that makes it a "sweet-smelling odour" in heaven, but the love involved in such a sacrificial act.
And what exactly makes it "such a sacrificial act" but His misery?
Satisfaction is about,
I. Justice, and the fact that God's justice demands satisfaction,
False. It's an arbitrary scale. God could remit any and all "satisfaction" owed without Him being unjust. In fact, that's exactly what the doctrine of Indulgences holds He does.
Especially noxious is the doctrine that this satisfaction can convert sinners, which entails that God can convert sinners via a simple act of His will, but refuses to do so until He gets His pound of flesh first.
II. Love, which can satisfy justice through imploring God's mercy, and this is the activity of the saints,
You are now saying, at least apparently contradictorily to I., that justice is satisfied through imploring God's mercy. OK, fine then, each of us does that every day when we say the Our Father (and the Jesus Prayer for those of us in the East).
But I'm also going to take issue with the implied assumption that mercy is something God may or may not grant, whereas He is Mercy itself by nature. You have a bimodal God, it seems, sometimes acting out of justice and at other times out of mercy.
III. Punishment, which is what happens to sinners who refuse to satisfy for sin through an act of sacrificial love, and this is especially the state of the souls in hell and in purgatory.
Except Jesus satisfied for all sin on the Cross, so theologians have to talk about merits being "applied" to say how their sins aren't really satisfied for despite the fact Jesus satisfied for them. It's against the nature of God to want to "get back" at the very humanity He created. Hell exists because these souls hate God and it is now metaphysically impossible for them to be otherwise. Purgatory exists as a state of final purification, not because God is childishly and vengefully exacting some "debt" He could nevertheless choose to remit.
If you think God is evil and foul for demanding retribution for evil, you simply lack a sense of justice.
If you think that God prefers to punish sinners rather than to see them repent and atone through love, you need to read the scriptures more.
These two statements are contradictory, and show how the idea of the "vengeful God" is a human construct, and a quite childish one at that, and one which belongs in the trash bin, which is where it is everywhere except in trad circles. True, it is a human sense of justice that wrongdoers be punished; valid in its own sphere (because society cannot function properly if they are not), but not when God is anthropomorphized in this fashion.
God can't return evil for evil; that is not His nature, as He
cannot be the author of any evil. Theology of hell has therefore moved on in recent years from the childish idea of the vengeful God to the reality that this is the natural consequence of sin - if you took a soul in hell and put it in heaven, it would be an even greater suffering, for they would be face-to-face with one they hate.
And I'm curious how this fits in with your Augustinian predestination, which you likewise justify through Scripture; God "prefers" to see sinners repent, but nevertheless refuses to cause them to do so, even though He could, since He made them "vessels of wrath".