re: Cornelius - He was baptised. Why is the Sacrament of Baptism necessary for those who have supposedly had their sins remitted? Because BOD by definition does not remit temporal punishment, does not confer the sacramental character, does not incorporate one into the Mystical Body of Christ, the Church. But we know also from the teaching of the popes that justification, since the promulgation of the Gospel (the founding of the Church) cannot be had without the Sacrament of Baptism.
Yes, on this points the Dimonds made a spectacular argument by way of syllogism from Church teaching. Initial justification is defined as a rebirth, and that rebirth is defined as remitting ALL stain of sin including temporal punishment. So an initial justification without the remission of all temporal punishment, i.e. St. Alphonsus' theory, is condemned from Church teaching.