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Baltimore isn't absolutely infallible though, and the strictest EENS people would say that it is wrong in the light of Florence.

Exactly, no one has to believe the catechism to get to heaven, while we 100% have to believe Florence.
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My issue at the end of the day is that I can't believe that the writers of ...(fill in the blank) are all just idiots who can't read the plain words of Florence, yet that is the logical conclusion of the *way* guys like Stubborn and Last Tradhican (lol that name is fitting here :D ) argue for a strict view of EENS.

Feeneyites don't see their opposition as "idiots" but as normal, human beings just like themselves, with a finite understanding of God's infinite wisdom, Divine Providence and His knowledge and capability to nudge/help all those who want to be saved.  Let us not forget that God will not save anyone against their will, nor does He cast into Hell those who desire Him.  But conversely, it is also true that there is only the straight, narrow path to God and broad is the way which leads to damnation.  So how do we, as finite beings, explain the complexities of the mystery of salvation?  It's impossible. 
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The main problem with BOD is that it opens the floodgates to our natural, human tendency to explain/understand the mysteries of the Faith in HUMAN TERMS, which includes emotion, sentimentality, and the horror at the doctrine of the "fewness of the saved".  And since we can't know the mind of God, nor His designs, all we can do is take our extremely, limited view of person A ("who's such a nice person") and we can't fathom that such a one would not love God to the extent that He requires, which is sanctity.  As Christ told us, "Be ye perfect as your Heavenly Father is perfect."  As St Paul tells us, "Thus is the will of God, your sanctification."  This requirement for sanctity and perfection is for all men, no matter their religion.  Thus, those that do not join the Church, cannot attain the perfection that we can only receive from Christ and His grace.  Thus, it is logical to lament the vast majority of souls who are not saved - all of those outside the Church and even the vast majority of we who are members.  So, BOD is often used because we cannot emotionally accept the fact that most are damned.  Even though Scripture, the Church and Christ tell us otherwise.
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As Fr Wathen often said, "Many people that go to hell are not bad people.  They were just not good enough to get to heaven." 
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This lines up with God's warning to all of us in the Old Testament:  "Be ye hot or cold.  The lukewarm I will vomit from My mouth."
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I'm actually not even *that* perturbed by the idea that they might be *right* (though I'm nearly certain Trent is teaching BOD as a possibility *at least* for the catechumen) as to the final conclusion. 

Trent never taught that an unbaptized, justified person goes to heaven.  Trent only said that an unbaptized person who (fulfilling the proper requirements) desires baptism could attain the state of grace.  Fr Feeney was just pointing out a theological problem that the Church has yet to clarify.  Many of those who came after Trent, as is human nature, interpret Trent in a liberal way, so that BOD "can save", because they *want* to believe that there is the possibility of salvation for their friends or family members.  But, technically, Trent did not say that they could be saved, only justified.  Fr Feeney never said that BOD was wrong, only that it's not certain. 
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My bigger issue is the argument.  Like, I'm admittedly a new convert.  And apparently I'm supposed to *absolutely* believe my own interpretation of Florence over what all the clergy say.  Like that, by itself, is a huge stretch.

Since BOD has never been taught doctrinally or "de fide", then it must be proved to be an "apostolic teaching" (i.e. from Tradition, or "what has always been taught").  Since the idea has been debated ever since the times of St Augustine, and since it is still debated today, then it is certain, beyond a doubt, that BOD is not unanimously held.  So it's not a doctrine, it's not part of Tradition and it's CERTAINLY not proven from Scripture.  So, when you speak of the opinions of "all the clergy" that is incorrect.  "Most" is not the same as "all".  And a theological opinion is not binding if it is only held by "most".
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And even among the "most" who believe in BOD, they do so with many differences.  So which type of BOD is "catholic"?  St Thomas' opinion?  Trent's?  St Alphonsus'?  The Baltimore Catechism's?  St Pius X's catechism?  Archbishop Lefbreve's?  V2's?  XavierSem's?  Praeter's?  They all have different explanations.  No one can point to THE source to explain the "doctrine".  Such confusion shows that it's not a Divine Teaching but is a theological opinion.  It has (understandably but wrongly) been invented (and accepted) by our emotional human natures as a "coping mechanism" to deal with the spiritual gravity, the eternal magnitude and the fear of God's all-knowing and just judgements, which are all part of the doctrine of the "fewness of the saved" and which no man can escape or minimize.

What are you implying here? That some may die "justified" and not be "saved"?

It's not an implication, it's a factual question that remains unanswered by the Church.  Even St Thomas could not explain how his BOD theory worked.  At one point he said that even BOD would not imprint the baptismal mark, so such persons would have to go to purgatory, since their temporal remission of punishment due to sins was not washed away.  Others have said that such persons would go straight to heaven, ignoring such "details".  I hold that a justified but unbaptized person (i.e. like an unbaptized baby) would go to the highest place in hell, (i.e. Limbo) and would thereby be rewarded for their desire with a place of natural happiness, since they are innocent but not members of the Church.  But they would not merit heaven since they didn't receive the sacrament.  I could be totally wrong; just my opinion.  But Trent does not clarify any of this.

I would be much more satisfied with BoD theory if it held that those who died in a state of justification were granted the character of Baptism by God in an extraordinary manner than that they could experience the Beatific Vision without it.  And, since all these aspects of BoD are pure speculation, what would stop me from speculating that God does exactly that?