2 Esdras (or 4th, Ezra) has already been noted by you as NOT endorsing Augustine’s interpretation of Original Sin.
This is a good example of the difference between “The Fall” vs. “Original Sin”!
Below i quote from you:
“But you did not take away their wicked heart and enable your law to bear fruit in them. For the first man, Adam, was burdened with a wicked heart; he sinned and was overcome, and not only he but all his descendants. So the weakness became inveterate. Although your law was in your people’s hearts, a rooted wickedness was there too; so that the good came to nothing, and what was bad persisted.”
Then you add:
“That account would be a completely unremarkable summary of original sin in Christian terms, including an Augustinian description of its inherited nature – missing out only the concept of inherited guilt for Adam’s sin…”
We have to remind ourselves that simply reciting the sequence of events is not the same as defending Original Sin:
1] It is a Biblical fact that Eden had the Tree of Life.
2] It is a Biblical fact that God’s punishment included no access to the Tree of Life (which isnt even mentioned as part of God’s listing of curses).
3] And it is a fact that God did not provide a provision for “re-testing” and “re-entry” to Adam’s offspring.
This is not “Original Sin”. This is the inevitable logistics problem of punishing the Father of Humanity without inconveniencing all of humanity.
The question you put is perfect: what about the supposed “inherited nature” of Original Sin?
The writer makes it clear that this is not Paul’s doctrine:
“…But You [God] did not take away their wicked heart and enable your law to bear fruit in them. For the first man, Adam, was burdened with a wicked heart…”