Are you unaware of Pius IX's discussion of "invincible ignorance?"
https://www.papalencyclicals.net/pius09/p9quanto.htm
"7. Here, too, our beloved sons and venerable brothers, it is again necessary to mention and censure a very grave error entrapping some Catholics who believe that it is possible to arrive at eternal salvation although living in error and alienated from the true faith and Catholic unity. Such belief is certainly opposed to Catholic teaching. There are, of course, those who are struggling with invincible ignorance about our most holy religion. Sincerely observing the natural law and its precepts inscribed by God on all hearts and ready to obey God, they live honest lives and are able to attain eternal life by the efficacious virtue of divine light and grace. Because God knows, searches and clearly understands the minds, hearts, thoughts, and nature of all, his supreme kindness and clemency do not permit anyone at all who is not guilty of deliberate sin to suffer eternal punishments."
If Pius IX thought it important enough to mention, why wouldn't it be important for the trad clergy to make that distinction as well?
The distinction Pius IX is making is between those who never held the Catholic Faith (because they were ignorant of it) and those who did, at one time, hold the Catholic Faith but fell away from the Faith and "are living in error."
Pius IX did not make the distinction in the same way clergy do today. In fact, I don't think the "distinction" Pius IX made is what you are claiming it is at all.
very grave error entrapping some Catholics who believe that it is possible to arrive at eternal salvation although living in error and alienated from the true faith and Catholic unity. Such belief is certainly opposed to Catholic teaching. There are, of course, those who are struggling with invincible ignorance about our most holy religion
Notice that, after saying that the belief that those "living in error and alienated from the true faith and Catholic unity" can "arrive at eternal salvation" is "certainly opposed to Catholic teaching", Pius IX does NOT say "however" or "but" or any other common beginning of EENS soft denial. He teaches the dogma as it is, and leaves it at that, and
then moves on to the invincibly ignorant.
And what does he say about the invincibly ignorant? Not what you claim, and not what trad clergy teach. He simply says "they live honest lives and are able to attain eternal life by the efficacious virtue of divine light and grace". Where in this quote do we read that the invincibly ignorant can be saved without formally entering the Church? Without explicit faith and baptism?
Those invincibly ignorant who live honest lives and observe the natural law will be furnished with the means of salvation. That must happen, in order for them to be saved, because the invincibly ignorant are included in those who "[live] in error and [are] alienated from the true faith and Catholic unity"! And what did Pius IX teach about those "living in error and alienated from the true faith and Catholic unity."? They cannot arrive at eternal salvation
Was it Pius IX that lamented liberals who twisted and misinterpreted his words?
Pope Eugene's comment also references those who do not "remain" in the Catholic Church, meaning that they were once Catholic and fell away from the Faith. See the word "remain" in your quote from Florence:
"The most Holy Roman Church firmly believes, professes and preaches that none of those existing outside the Catholic Church, not only pagans, but also Jews and heretics and schismatics, can have a share in life eternal; but that they will go into the 'eternal fire which was prepared for the devil and his angels' (Matthew 25:41), unless before death they are joined with Her; and that so important is the unity of this ecclesiastical body that only those remaining within this unity can profit by the sacraments of the Church unto salvation, and they alone can receive an eternal recompense for their fasts, their almsgivings, their other works of Christian piety and the duties of a Christian soldier. No one, let his almsgiving be as great as it may, no one, even if he pour out his blood for the Name of Christ, can be saved, unless he remain within the bosom and the unity of the Catholic Church."
-Council of Florence
Pope Eugene would not say "pagans", "Jews and heretics and schismatics" if he was speaking of Catholics, because none of those people are Catholic. Again, note that he made no distinction between pagans, Jews, heretics, and schismatics who are invincibly ignorant and those who are not. They will all go into the eternal fire unless, before death, they are joined with the Church. If they are joined with the Church before death, they are no longer pagans, Jews, etc.
The usage of the words "remaining" and "remain" appear AFTER Pope Eugene says that those listed above must be joined with the Church in order to be saved. You must be joined with the Church AND remain in Her unity in order to be saved