a fourth baptism called baptism by illumination. ....But just look how far these theologians go and how much confusion they sow among the laity.

Why not?  Isn’t a baby “sincere” in his love for God?  A baby can’t sin against God, so they are conceived with an implicit love for God, right?  And if they can’t sin, isn’t their love of God as “perfect as it can be”?  
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Is it the baby’s fault that they died?  Of course not.  If they had been born, they would’ve been baptized, right?  They would’ve had a chance to love God, right?  So how can they be penalized for dying?  Surely they go straight to heaven.  (Modernism thought process is finally over).
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If you believe any part of the above, then you might as well believe what the Mormons believe and go to their temple and have your ANCESTORS baptized.  It follows the same logic.

You keep repeating the assertion that Pius IX and the Catechism of St. Pius X teach the possibility of salvation by implicit desire.  But even Dulles, an EENS laxist, asserts that Pius IX COULD HAVE MEANT that additional grace is needed for justification/salvation.  There's no "could have" about it.  He clearly says that these types will be saved by "LIGHT" (the opposite of ignorance).  And Pius IX denounced YOUR VERY INTERPRETATION of his teaching as an "atrocious injustice" to him.  Same thing is true of St. Pius X who deliberately uses the term that these are "on the way" of salvation.  There's simply nothing there.  But then you reject the teaching of St. Thomas, St. Robert Bellarmine, and St. Alphonsus regarding the need for explicit faith.  You reject the 1703 Holy Office rejection that explicit belief in the Holy Trinity and Incarnation are not required by necessity of means for salvation.  You're a hot mess.

Contradictions and confusion are a sign of bad will.

Well, you said it, not me. Are your contradictions also a sign of bad will?

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No it doesn’t.  The question was “can non Catholics be saved?”  The answer was not clear.  It said they can be “on the road to salvation” if they do x, y and z.  It was a non-answer.

In English, it says "or at least has the implicit desire of Baptism". If you want to argue that "implicit desire of Baptism" is something different from "implicit Baptism of desire", then say so. Whatever that has to do with salvation is a separate thing. 

You’re missing the point.  Being “saved” in a false religion is not equal to being “on the road to salvation”.  The catechism is describing the circuмstances for one to LEAVE their FALSE religion and JOIN the CHURCH.  

To be fair to Stanley, you and Lad have not responded to Q 17 in Pius X's Catechism (only Q 29):

Q17. Can the absence of Baptism be supplied in any other way?

A. The absence of Baptism can be supplied by martyrdom, which is called Baptism of Blood, or by an act of perfect love of God, or of contrition, along with the desire, at least implicit, of Baptism, and this is called Baptism of Desire.

The "on the way to salvation" mentioned in Q29 may mean that such a person must also have the act of perfect love of God or act of perfect contrition mentioned here, not just implicit desire for baptism.

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From the Catechism of Pius X:

Q29. But if a man through no fault of his own is outside the Church, can he be saved?
A. If he is outside the Church through no fault of his, that is, if he is in good faith, and if he has received Baptism, or at least has the implicit desire of Baptism; and if, moreover, he sincerely seeks the truth and does God's will as best he can such a man is indeed separated from the body of the Church, but is united to the soul of the Church and consequently is on the way of salvation
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Ok, so let's look at the problematic phrases, which are open to interpretation (and which Modernists like Rahner, Dulles, etc) all used in their successful attempts to water down EENS to pave the way for V2's ultra-heresies.
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1.  Good Faith - what is this?  How is it defined?  How does one know who has it or not?  None one knows.  It's subjective, it's open-ended, it's open to sentiment and emotion.
2.  Implicit Desire - what exactly does this mean?  Is this St Alphonsus' implicit desire?  Or Rahner's "anonymous catholic" version?  It's not precise at all.  Dangerous theology.
3.  Sincerely seeks the truth - This seems pretty straightforward, right?  Except that only God knows who is sincere or not, since none of us can read hearts.  So, again, dangerous theology.
4.  God's will as best he can - Same as above; only God can know this.  Doctrine is black and white.  This is theological opinion and is dangerous for most people to think about.
5.  On the way of salvation - What does this even mean?  A liberal/modernist would define this as the person can "be saved in his current non-Catholic state".  An orthodox/traditional catholic would say that this means the non-Catholic is "progressing towards the full truth of the Church, which God will give to him, if he continues searching."
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Do you see the MAJOR DIFFERENCE between these 2 interpretations?  Do you see the major problem with imprecise language?  Don't you see how this was the exact same method used at V2?
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Yes, I do. I am definitely beginning to question this.

The scenarios where someone dies for the Faith are so remote that I don't waste time on baptism of blood.
You can't mix-and-match catechism answers to make up your own theology.  If you want to know, definitively, what is required for BOD (and by extension, BOB) then go read Trent on justification and preparation for Baptism.  Trent lays out the spiritual requirements necessary to join the Church - EXPLICIT FAITH, sorrow for sins, a change of life, and a desire for baptism.  This is exactly what St Thomas said.  More or less, it's what St Alphonsus said.  Anything or anyone who preaches something less is anti-Trent.

But you still haven't responded to the reference to implicit desire in Q17 of Pius X's Catechism.