I don't know why you are doing this over here but once again, some of the quotes from the ECF's do indicate penal substitution. And PSA is satisfaction atonement but with a more developed theme of justice and punishment. And, the idea of moral influence of the atonement is completely compatible along side PSA, just not as the core of our atonement.
They do indicate a type of penal substitution.
They held that Jesus had died in the place of "the whole human race" bearing man's and the punishment of Satan that man justly earns, so that man would be reconciled to God and be cleansed of sin.
I will admit you could say that is a type of penal substitution, and that that beluef would fit into your definition.
The problem is the actual belief is not PSA. When defining PSA its holders have devolved into making their own belief benign and generic, probably because it has been declining over the last couple of decades.
Paul Enns offers a good definition:
Jesus Christ willingly took humanity's place on the cross, bearing the penalty for our sins, satisfying God's justice, and allowing for our forgiveness and reconciliation, with Christ being our legal substitute before God's judgment.
But nobody would confuse the Early Church as believing this definition.
The reason the Classic view was introduced is you offered a generic atonement as defining PSA. I was saying every Christian, even those who do not hold PSA, would hold your definition of it.
PSA really has a meaning that distinguishes it from other views.