We have St. Robert Bellarmine, St. Alphonsus, and even Father Feeney taking it the second way.
We have an advantage over St. Bellarmine and St. Alphonsus, because they didn't have Vatican 1. Meaning it wasn't so clear which decrees were infallible and required the assent of Faith, and which ones did not. Perhaps they mistakenly thought Pope Innocent II's BOD teaching was infallible, and they had to reconcile that with Trent. Now we know it wasn't, and is in fact wrong. Those examples you provided aren't comparable, because they fail to take into account the context of Session 6 chap. 4, particularly "AS IT IS WRITTEN, John 3:5", and the rest of the chapters of the session, which completely ignore "BOD". If a text is ambiguous, we should base our understanding of it on the context.
St. Alphonsus also taught that BOD does not provide the grace of spiritual rebirth/baptism, which Trent says everyone must have to be justified.
Here is Trent's teaching:
Council of Trent, Sess. 6, Chap. 3: “But though He died for all, yet all do not receive the benefit of His death, but those only to whom the merit of His passion is communicated; because as truly as men would not be born unjust, if they were not born through propagation of the seed of Adam, since by that propagation they contract through him, when they are conceived, injustice as their own,
SO UNLESS THEY WERE BORN AGAIN IN CHRIST THEY WOULD NEVER BE JUSTIFIED, since by that new birth through the merit of His passion the grace by which they become just is bestowed upon them.”
Here is the teaching of St. Alphonsus that BOD does not remit the liability of punishment due to sin, meaning BOD does not give someone a spiritual rebirth, without which no man can be justified:
St. Alphonsus: “
Baptism of blowing is perfect conversion to God through contrition or through the love of God above all things, with the explicit desire, or implicit desire of the true river of
baptism whose place it supplies (iuxta Trid. Sess. 14, c. 4) with respect to the remission of the guilt, but not with respect to the character to be imprinted, nor with respect to the full liability of the punishment to be removed: it is called of blowing because it is made through the impulse of the Holy Spirit, who is called a blowing.” (St. Alphonsus,
Moral Theology, Volume V, Book 6, n. 96)
So, do you agree with St. Alphonsus that BOD does not give the grace of a spiritual rebirth? Would you then hold that a man can be justified without being born again in Christ, contrary to Sess. 6, Chap. 3?