If we understand Trent Session 6, Chapter 4 to not be teaching BOD, then our reading and understanding of Trent is contrary to how St. Alphonsus and St. Robert Bellarmine's read and understood the same words.  Either we aren't understanding Trent correctly, or both St. Alphonsus and St. Robert Bellarmine didn't understand Trent.

No, the "subsists" argument is heresy because it cheapens the definition, solemnity and truths of the "Church of Christ".  To be with Christ, you must hold ALL of His Divine Truths; not 90% or 70%.  Christ cannot be divided so that we can say that His Church is part over here but fully over there.  As He told us, "He who is not with Me, is against Me."  We must accept the WHOLE Christ, not just part of Him.  There are certainly truths of the Church which non-Catholic religions hold, but it is heresy to describe these truths as "salvific elements" (for they can in no way save anyone, just like half of a car engine cannot run).
.St Augustine and St Thomas agree wholeheartedly in this.  They also agree with Trent.  V2 agrees with them, but then contradicts itself using the "subsists" phrase.  This ambiguity is heresy because the Church, and all Catholics, have the duty to preach the pure, unadulterated Truth, at all times, in all circuмstances.

Logically, if the modernists used the term "salvific element" but then say, as you do, that it doesn't mean these "elements" can save, then the use of the term "salvific" is contradictory, confusing and heretical.  The reason why they used the term is PRECISELY to IMPLY that such elements CAN save.  The liberals use this phrase to teach 'universal salvation' to their 'protestant brethren' and to further the heretical, one-world, new age ecuмenism.
. Nowhere in V2 is this made clear.  So, if one reads V2 by itself, one can easily be led to believe that one can be saved outside the Faith.
.Le'ts say that Catholic Doctrine = A.  Heresy does not have to say "not A" or "I completely reject A" or "A is wrong".  Heresy can simply be "A + part B".  Or "A + Z" or "A minus C".  You are defining heresy in too strict of terms.  Heresy is any addition, deletion, edit, implication, or alteration of Dogma (however small).
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To say that the Christ's Church "subsists in" the Catholic Church is heresy.  Pure and simple.  The Catholic dogma = Christ's Church IS the Catholic Church.  
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To imply, as V2 did, that Christ's Church ALSO exists partly in other religions is heresy.  You can say that certain truths exist in other religions, but these truths are not equal to Christ's Church, which by definition, is ALL Truth and the FULLNESS of truth.
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As an example, if you mix together Kool-Aid with water, you get a new drink.  You can say that a Kool-Aid mix "subsists in" the water, but you cannot say that water "subsists in" the Kool-Aid.  This is backwards.  There is no Kool-Aid without water but there can be water without Kool-Aid.
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In the same way, Christ's Church is made up of ALL the Divine Truths of the Faith.  You can say that the Divine Truths "subsist in" Christ's Church, but you cannot say that Christ's Church "subsist in" the Divine Truths.  This is backwards.  The Divine Truths may be partly believed outside of Christ's Church, but you cannot have Christ's Church without the FULLNESS of Truth.

You don't have this impression because you know your Faith and you are interpreting this phrase in a traditional light.  Those that don't know their Faith, and those who are modernist heretics, can use the phrase "salvific elements" to argue that V2 teaches that those non-Catholics who are "sincere" can be saved.  In fact, that sincerity and good will can save, is said by V2 in its other docuмents (I forget which).
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The correct phrase should've been "truthful elements", in that, some non-Catholic religions have some truths in them.  This is obviously correct.  If these elements have nothing to do with salvation, as you argue, then the term "salvific" is unnecessary.  Why was it used?  Of course, it was put in there by modernists so that they can use this phrase, along with other phrases like "sincere" and "ecuмenism" and "good will" and "religious freedom" to spin together the story that non-catholics can be saved.  And they've spun this story well and V2 is the leading reason why 99% of population will accept the coming one-world-religion.
.If the phrase "salvific elements" has nothing to do with salvation, then why use the word "salvific"?  You make no sense.  Your argument is silly.  It's plainly obvious.
.If a salvific element doesn't save, then it's a contradiction in meaning.  If a salvific element of the protestant religion can save outside of the Catholic Faith, then that's heresy.  So the phrase, as it's used in that V2 passage, is either illogical nonsense or heresy.  Pick one or the other.  Either way, it is wrong.
.You are like most conservative catholics who try to read V2 in a positive light - you infer things which simply aren't there.  You ignore plain English and interpret a traditional meaning, whilst ignoring the obvious heretical problems.
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Non-catholic religions have certain Divine Truths; they do not have ANY salvific elements.  They cannot save, period.  V2 says they have both.  If V2 had simply said that some Divine Truths are contained partly in non-catholic religions, fine.  But it went beyond this boundary and implied that a religion with only PART of Divine Truth can save.  Again, as it is written, in plain English, this is either illogical, imprecise, faulty theology or it's heresy.   You choose.  Either way, it's wrong.

This passage is heretical because it subtly and devilishly splits the “Church of Christ” from the “Catholic Church” and explains them as 2 different things, when in fact, doctrinally, they are one and the same.  
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It says that the Catholic Church is the visible society where Christ’s Church is organized, but ...it then heretically implies that Christ’s Church, HAS AN INVISIBLE SIDE TO IT, which is apart from the visible, Catholic Church.  Then it further heretically says that there are “sanctifying” elements in this non-visible, non-Catholic, Church of Christ.  This is total modernist garbage.  
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The Church of Christ is the Catholic Church.  Both visibly and invisibly.  They are one and the same, in degree, and in all things.  There is no Church of Christ without the Catholic Church and there is no Church of Christ outside, invisible, apart or in addition to, the Catholic Church.  You cannot separate these 2 ideas.  Those who wrote such things are anathema.  

There is no such thing as a Protestant baptism because baptism is a catholic sacrament.  There are only catholic baptisms performed by Protestants.  Yet baptisms can be even performed by atheists, Jews and heretics too.  So there is no contradiction.
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When one is baptized by a Protestant, they become 100% catholic and are part of the visible church, who, because God in His Providence decided to bestow this sacramental character on the person, they are now under the spiritual authority of the pope.
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Only when the person grows up, and rejects the Catholic Faith (by accepting Protestant heresies) is the person then a schismatic and is guilty of rejecting the Truth.  
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But all valid baptisms are Catholic baptisms.  A Protestant baptism would be a parody of it, using incorrect words or only being immersed/dunked in water and then only generally “accepting Christ”. This is obviously invalid and baptism doesn’t occur.

Christ obviously acts beyond the Catholic Church, trying to get people to the one true Church. 

Just associating with those sanctifying elements cannot save, though,

I'm trying to argue that there may be SOME way to reconcile V2 with tradition, but it's only really a logical possibility, and not one that I can even entirely believe. But it's still POSSIBLE.

The valid Bishops of the Church still provide unity of Communion and Government, methinks, even in this era of confusion.