To put it simply: I'm getting from you guys that you might argue that PSA makes nonsense of the word "forgive" and instead substitutes that the punishment of the crime was simply paid by another (an innocent in this case, being Christ). Thus God "forgave" nothing.
No, you missed a vital point.
PSA basically assigns that Justice demands God's wrath be extinguished by being poured out. Yet, that is not the presentation of Scripture.
The wrath of God does not extinguish the need for justice or none would go to the eternal lake of fire which leads some to conclude that PSA is actually universalism and/or that it has the teaching of a purgatorial thinking of the lake of fire in which eventually everyone ends up in heaven.
Forgiveness is not to be tied to a demand for justice, but to satisfaction of a pleasing sacrifice.
For example, in all the sacrifices and offerings in the OT temple/tabernacle the single emphasis was upon the satisfaction. Without the satisfaction no amount of blood, grain, drink or whatever was acceptable.
We see in Colossians 2 how God was satisfied, and in Hebrews 9 the steps Christ took to accomplish that task.
Now, what if one does not believe?
Then there remains no forgiveness, but after death comes the judgement.
What if one believes.
Then there is no condemnation, but we have passed from death to life.
Where is the wrath of God?
See Rev. 16.