That last paragraph is important.  Now one criticism the anti-BoDers get is that we deny God's will to save all people, and that everyone must have the active concrete opportunity to be saved.  So I always ask about the unbaptized infants.  What about them?  I always get crickets in reponse.  Then I explain as you did that God's Mercy made it so they ended up in a place of perfect happiness because foresaw that if they had received the gift of faith they would have been damned and would suffer forever in Hell.

Check the post you're referencing here again, bud.  That's what.  You'll notice that I was NOT responding to you but to QABrownson1876's comments.  He was describing Orestes Brownson's position, to which I threw in my own observations.  Despite your ego believing that I was responding to you, I didn't even read what you wrote, because quite honestly I don't care about your opinion.

So what if Brownson believed in an explicit Baptism of Desire?

It's for that reason that I hold there to be a huge surge in abortions, with 73 million per year worldwide, every year now for many decades.  We're approaching quickly a billion aborted infants ... and they will all enjoy perfect natural happiness forever.  What a great Mercy from God ... because in this wicked, corrupt world, especially if you were to be born to and raised by parents who would think nothing of murdering you, your chances for salvation are slim to none anyway, so the less a chance people have of being saved, the more you'll see them being aborted and going to Limbo for eternity ... where they will praise God in perfect bliss for His Mercy through all eternity.

Because salvation is a gift, no one deserves it.

I believe that the biggest animus working against the acceptance of EENS dogma has been this strange monolithic view of Hell, where some naturally virtuous Jєωιѕн grandma, who maybe even lays down her life for her grandchildren, ends up burning in Hell right next to Joe Stalin, in some monolithic cauldron of fire.  But even one of the Catholic EENS definitions explains that each individual's punishment is commensurate to his sins.  We all know some naturally virtuous, genuinely kind and generous people who die without the faith, so do those people get hurled into a cauldron of fire to be burned forever next to the serial murderers who are also there?

This is typical Newchurch muddle-headedness, to imagine that hell is equally bad for everyone.

We can't confuse some "sincerely wanting" with having the will, intention, and desire to do something.  It also depends on his motives.  Sure, who doesn't want to be happy forever?  But is the person WILLING to do what it takes and does the person actually love God, or just want something for himself.  That's one of the worst problems with this notion of Baptism of Desire.  Latin word mis-translated as simple desire is votum, which is more like a vow, an act of the will (word derives from willing something), and even Catholic Encyclopedia states that this term refers to having all the dispositions indicated by Trent as necessary for receiving the Sacrament.

With that said, if God allows someone to be invalidly baptized, He has His reasons, just like He has His reasons for having various people die as unbaptized infants.  If God willed this person to have the Baptism corrected, then He'll take care of it, bring its invalidity to light, or even work some extraordinary and miraculous thing.  There was such a case in the life of St. Peter Claver, where a woman had been a devout Catholic for years, a daily Communicant, etc.  She died without the Last Sacraments.  St. Peter was inspired to raise her back to life because he knew something was amiss.  So he started to hear her confession and then suddenly received the light that she had never been validly baptized.  St. Peter baptized her, and then she died.  Now, this woman reported to St. Peter that after she died she was told at one point that she could "go no further" due to lacking the wedding garment.  So here's a woman who had been a devout daily Communicant and evidently her sincere desire and intention to practice the faith did not suffice for entry into the Kingdom.  But sine she was among God's elect, He took care of the problem, in this case miraculously.  He'd do the same as needed for anyone else, perhaps bilocating someone to that person's side in his last moments, or having an angel baptized the individual (nothing to prevent that ... so what's the need for "BoD"?), or simply work in an ordinary way by (as happened in a couple cases in the United States), having some video come to light where this deacon had been baptizing invalidly for decades.

This kind of speculation here never ends well.  We simply trust God that everything He does is the most Merciful and most Just thing He could possibly do.  And that's all we need to know, and it's nefas to inquire further.

When I speak of someone who sincerely wants to be saved, I am speaking of someone who has faith and seeks to fulfill God's will and sanctify himself, who prays the Rosary every day, goes to Mass regularly, etc. If this person does not fall into mortal sin, will this person necessarily be saved? Is it possible that God will still refuse him salvation? Will this person learn by surprise at death that he was not baptized and then, too bad for you?