Unbaptized Children, Hell, and "Let the children come to me..."

Amici, FWIW, and to save some the trouble of deep digging for answers to the question of what happens to unbaptized chidren, some ponderings...

• Preamble 
  Our Lord is clear in the Gospels: those who don't believe in Him are lost. However, as for children, He said let no one prevent them from coming to Him (Matt 19:14). This passage clearly means first, at that exact point in time, and also (we can clearly deduce) for the rest of his Earthly ministry: "Apostles, let the kids come to me; don't hinder them."
  Second: Traditionally, and no doubt truly, the Church interprets this passage as meaning anyone who wants Salvation must have the clear, innocent, beautiful Faith and love (charity) children have. (Cold calculations, measuring everything to a finely balanced metric, don't cut it.)
  Third: "Such is the kingdom of Heaven" – considering that these were as of that moment unbaptized Jewish kids, it is highly probable indeed that He truly meant ALL children were His, for He made 'em, knows their destiny (whether they become adults or not) and so on. Remember, when God says X, X happens. All Creation was created by the Father through the Son (the Logos) so I think it reasonable to understand Our Lord Jesus, Joshua, "Yahweh Saves", is proclaiming here that children will be saved.
  Don't know it for sure, of course, but it makes sense.
  So an answer: Trust God. If one is going to believe in the Christian God, He went to literally infinite trouble to become a human being, amazing the good angels (and of course confounding the bad ones) and redoing Creation on the off-chance (as it were) that some (small or large, probably small) portion of His human creation wouldn't deny Him. He was Incarnated in us so we could be incarnated in Him, through His grace ("grace" meaning "gift".) If He enabled the Immaculate Conception, as a pure gift (grace) through his not-yet-at-that-time Incarnation, He can save unbaptized infants. He's Lord of the Sabbath, in short; the Sabbath (here standing for Fallen Humanity, and Creation, and the curses of the Fall, etc.) is not His master.
  The BVM: The Blessed Mother. She is our great Advocate. And she's a mother. Does anyone think she wouldn't advocate for children who no fault of their own were not baptized? Does anyone think He would deny Her?
  Protestants and Orthodox: I suppose Prots are all over the map with answers to this. Most of the ones I've ever known think all kids go to Heaven, as a matter of course. The Orthodox Churches (14 independent "Ghetto" Churches), deny the Catholic teaching that unbaptized infants go to Limbo. But then, they've made an absolute mush of Purgatory, and trashed out a number of other things, like divorce and remarriage, so "whaddatheyknow"?
  Robert Bellarmine, much in the news because of his teachings about bad popes, was the last major Catholic thinker to teach that unbaptized infants went to the Hell of the Damned. Aquinas, Vulcan Academy-trained in logic, taught unbaptized infants didn't go to Fiery Hell, but a mild and happy Limbo, and his position eventually carried the day, but the Church has never actually dogmatically defined this.
  An Préachán