I really enjoyed reading this, as I haven't seen such a well-argued and documented debate between Augustine and the Stoics.
The difference between the two seems pretty evident to me when I take their religious views on the afterlife in account.
Augustine, a staunch purveyor of Christianity around 350-400 AD, perhaps the most influential theologian to promote Western Christianity, believes in the afterlife. Christian belief will pose that the flourishing of the eternal soul throughout the afterlife is far more important than one’s single human life. Thus, his reasoning for flourishing is going to derive from that belief.
The Stoics were not Christians and even rejected the concept of an afterlife. Their idea was that flourishing or happiness was exercised through virtue within one’s human existence, and after that it was over. So naturally they are going to reason from that perspective.
While Augustine and the Stoics do agree on some things as you illustrated, I cannot see how they could possibly agree ultimately on this topic when they operate with incompatible mindsets pertaining to temporality and planes of existence. I’ve seen this difficulty echo throughout all of philosophy. Even when studying the existentialists, debates often reach a stalemate when some thinkers are taking God in account and some are not. It’s apples and oranges.