The election of the saved being a gratuitous act of God's predestination being a truth of Scripture and the Church's teaching, there is no ground for valid objection to God's conjoined free and gratuitous determination of the how or manner He does it.
Yes, indeed. And that's St. Alphonsus' second answer (quoted in your Reply #3), which he deems
more correct than his first one. I think, it should answer every and all questions of those who don't understand how Our Lord can "refuse" the beatific vision to unbaptized children who die before the age of reason. As a matter of fact, Our Lord doesn't refuse the beatific vision, in the same way the holiest of the Saints doesn't earn it.
Typically, this doesn't convince contemporaries, though, who think in terms of "human rights" and who don't think of fallen man in terms of "enemy of God". An unbaptized man is an enemy of God, ever since original sin (see Council of Trent, cuм hoc tempore, on justification). Many people imagine a father, who would be considered unjust, if he'd elect his first three sons to inherit all property, and let the rest go disinherited. They factor out the question of original sin, they factor out that the topic is about criminal children, who lost their rights as children, in the first place.
There was a comment on CI, about abortion. The commentator thought that (beside crying to heaven) it's a particularly evil crime, because the aborted child "will be denied the Beatific Vision for eternity". As if a man could cross the plans of God, who ensures that all who are called and chosen will make it to heaven.
But let me comment: if one understands predestination - God's willing and providing - being the infallible cause of - the salvation of His chosen elect, and understands the truism that God determines the means and the ends of everything He "simply" wills (St. Thomas, above), then the difficulties or problems of the "fairness" of God saving only those who are joined to the Catholic Church disappears: if He wills infallibly the salvation of all who are saved (and He does), it is obvious that He would also at the same time determine the how or the way He does it (i.e., do it in the manner He selected or wishes) - via faith in Christ, the Church, or baptism, etc.
One could no more object to His choice of how He saves than one can object to His choice of who is saved. The truth of one being established (God's choice of who is to be saved), their are no logical or legitimate grounds to justify an objection to the how, since both come down to His free determination and choice.
There is simply no distinction between the who and the how of election that legitimatizes an objection to the one rather than the other.
I agree. But I don't have much hope that many people will be convinced by learning that not having been baptized before death implies neither having been chosen nor been elect.