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Maybe I don't follow you. Baptism truly is the instrumental cause of justification, and we know this because Trent teaches so with the same authority it teaches no man can be justified except through/ without baptism or a desire for it.
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The nature of an instrumental cause is that something else can be substituted for it. That's what makes it an instrumental cause as opposed to a principal cause (instrumental and principal causes are two types of efficient causes-- see Aquinas's explanation above).
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While the meaning of "without baptism or a desire for it" might be arguable in a vacuum, the meaning of "instrumental cause" is not.  I therefore think it quite apt, knowing baptism is the instrumental cause of justification, to understand "without baptism or the desire for it" to mean that justification cannot be effected in a man who desires water baptism but who has not yet received it. This is consistent with it being an instrumental cause, whereas to maintain that no one can be justified without desiring to be baptized by water and then actually getting baptized by water is inconsistent with it being an instrumental cause.

It helps when the terminology used is the same as that used in the Church's teachings  - see bolded.

Note the contrary meaning Mith's post takes on when the teaching is misquoted as Mith (mistakenly?) did. Yet, correcting the quote according to the teaching by simply re-inserting the bolded words "without" and "cannot," we see within the Church's wording not only the unchangeability of it, but also the teaching's true meaning, which btw, Mith (underlined) expresses very clearly what the true teaching of the Church is.

"While the meaning of "without baptism or a desire for it" might be arguable in a vacuum, the meaning of "instrumental cause" is not.  I therefore think it quite apt, knowing baptism is the instrumental cause of justification, to understand "without baptism or the desire for it" to mean that justification cannot be effected in a man who desires water baptism but who has not yet received it. This is consistent with it being an instrumental cause, whereas to maintain that no one can be justified without desiring to be baptized by water and then actually getting baptized by water is inconsistent with it being an instrumental cause."

Stop being such a Freudian. Earlier in the thread Clemens Maria sourced an article arguing that the frequent translation we receive of "except through" is better translated as "without." I included both expressions to acknowledge this disagreement and not get bogged down in translational minutiae (which in my experience often ends discussions). Clearly I shouldn't have bothered with this courtesy, so for demonstrating that I thank you. 

Anyone claiming that sine doesn't mean without is just a plain liar.

https://www.online-latin-dictionary.com/latin-english-dictionary.php?lemma=SINE100
http://latindictionary.wikidot.com/preposition:sine
https://en.wiktionary.org/wiki/sine#:~:text=From%20Latin%20sine%20(%E2%80%9Cwithout%E2%80%9D).

Anyone claiming that sine doesn't mean without is just a plain liar.

https://www.online-latin-dictionary.com/latin-english-dictionary.php?lemma=SINE100
http://latindictionary.wikidot.com/preposition:sine
https://en.wiktionary.org/wiki/sine#:~:text=From%20Latin%20sine%20(%E2%80%9Cwithout%E2%80%9D).

I'm not sure I entirely agree that the label of "liar" applies to anyone, perhaps we can say it applies to anyone remaining obstinate after it's clearly explained, but even then, I think it goes much deeper than that. 


I liken this matter to the below snip on the EENS dogma from "Who Shall Ascend?" 

"...He who has ears to hear, let him hear." (Mt. 11:15, 13:9, 43). Jesus was aware that in the crowds He addressed were some who would be saved. They would be saved because they would find faith in Him by the power of the Spirit, through Whom they would recognize the divine truth which He spoke. Moreover, again by the power of the Spirit within them, these would respond to the truth which they recognized with the assent of faith and the grasping of joyful love.

Others who listened to Christ heard exactly the same words, but did not have the "ears with which to hear;" that is, they would not accept the grace to believe the truth which Christ expounded; for these latter, it had neither comprehensibleness nor urgency nor appeal. It might be better to say its meaning was both comprehended and its demand recognized, [but] The reason Christ's words were not accepted by most of His hearers was that they were unwilling to submit to its demands..."

Reading meanings into words which the words they read do not say, while failing to advert to what the words do say, I liken to Fr. Cekada, who openly admitted that he was unwilling to accept EENS because he knew most people were unwilling to submit to it's demands and would be lost forever. BODers are unwilling to accept the truth for the same reason.