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BoD per se (i.e., that there is such a thing as BoD) is infallible Magisterium.

False.

As I've pointed out, there are two possible readings of the crucial text.  We're debating which one is better.

Even IF the BoDer interpretation is correct (and there's no way I see it because, as I pointed out, the logical corollary is a heresy), Trent would be saying that there can be no justification without the Sacrament or the desire.  Trent never taught that justification can happen by the desire alone, but is effectively saying that you have to have the Sacrament AT LEAST IN DESIRE (leaving open the possibility).  There's nowhere any positive teaching in that regard, that the desire alone suffices.  In other words, it would be saying that you have to say that the Sacrament is necessary at least in desire to avoid the heresy of denying the necessity of the Sacrament.

But the BoDer intepretation is certainly false.  If you say that justification can happen WITHOUT the Sacrament, that's the very heresy being condemned throughout the treatise on justification.

"I cannot write a letter without a pen or a pencil."  This means that I CAN write a letter WITHOUT a pen (if I have a pencil).  CAN I be justified WITHOUT the Sacrament of Baptism?  Absolutely not.  Even if you believe in BoD, you can't say that this magical "BoD" process can happen WITHOUT the Sacrament.

My reading of the text ("the desire for [the bath of regeneration]" from Trent Session 6, chapter 4) is supported by commentary from St. Ambrose, St. Augustine, St. Thomas Aquinas, St. Alphonsus, by the Catechism of Trent, and by the "common opinion" of the theologians as discussed in Ott's Fundamentals of Catholic Dogma. 

Which Catholic theologians, teaching with an imprimatur, after the Council of Trent support your position? 

Also false.  Not only do theologians not "settle" anything (as they're not part of the Ecclesia Dicens), the theologians remain in disagreement on the most fundamental points about BoD.  We have no idea what it is, and we cannot give our assent to a vague ill-defined concept, only to propositions.

So, let me ask you this. Is the requirement of explicit faith in the Holy Trinity and Incarnation and Our Lord Jesus Christ necessary for justification?

The answer to your question about what kind of "faith" is required for Justification is in the passage on "Preparation" that we had discussed earlier from Session 6, Chapter 6:

CHAPTER VI.

The manner of Preparation.

Now they (adults) are disposed unto the said justice, when, excited and assisted by divine grace, conceiving faith by hearing, they are freely moved towards God, believing those things to be true which God has revealed and promised,-and this especially, that God justifies the impious by His grace, through the redemption that is in Christ Jesus; and when, understanding themselves to be sinners, they, by turning themselves, from the fear of divine justice whereby they are profitably agitated, to consider the mercy of God, are raised unto hope, confiding that God will be propitious to them for Christ's sake; and they begin to love Him as the fountain of all justice; and are therefore moved against sins by a certain hatred and detestation, to wit, by that penitence which must be performed before baptism: lastly, when they purpose to receive baptism, to begin a new life, and to keep the commandments of God. Concerning this disposition it is written; He that cometh to God, must believe that he is, and is a rewarder to them that seek him; and, Be of good faith, son, thy sins are forgiven thee; and, The fear of the Lord driveth out sin; and, Do penance, and be baptized every one of you in the name of Jesus Christ, for the remission of your sins, and you shall receive the gift of the Holy Ghost; and, Going, therefore, teach ye all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost; finally, Prepare your hearts unto the Lord.

I follow what Trent says.