The evidence that the two Missals are irreconcilable isn't only asserted by staunch traditionalists. It's asserted by non-Popes such as Fr. Gelineau, and by Popes such as Francis.

Pope Paul VI : Address to a General Audience, November 26, 1969
...liturgical innovation of the new rite of the Mass.
...a change in a venerable tradition that has gone on for centuries.
...something that affects our hereditary religious patrimony, which seemed to enjoy the privilege of being untouchable and settled. It seemed to bring the prayer of our forefathers and our saints to our lips and to give us the comfort of feeling faithful to our spiritual past, which we kept alive to pass it on to the generations ahead.
...We shall become aware, perhaps with some feeling of annoyance, that the ceremonies at the altar are no longer being carried out with the same words and gestures to which we were accustomed—
...We must prepare for this many-sided inconvenience.
...It is the kind of upset caused by every novelty that breaks in on our habits.
...We shall notice that pious persons are disturbed most
...Even priests may feel some annoyance in this respect.
...This novelty is no small thing. We should not let ourselves be surprised by the nature, or even the nuisance, of its exterior forms.
...As intelligent persons and conscientious faithful we should find out as much as we can about this innovation. (NOTE: WE ARE ALL DEFINITELY DOING THIS!!!!)
...we shall do well to take into account the motives for this grave change. (NOTE: we are trying to do well to take into account the motives, you can be sure.)
...This moment is shaking the Church, arousing it, obliging it to renew the mysterious art of its prayer. (NOTE: The irony of this statement is that the church has definitely been 'aroused' and is renewing (returning) to it's tradition!)
...It is here that the greatest newness is going to be noticed, the newness of language. No longer Latin, but the spoken language will be the principal language of the Mass. The introduction of the vernacular will certainly be a great sacrifice for those who know the beauty, the power and the expressive sacrality of Latin.
...We are parting with the speech of the Christian centuries; we are becoming like profane intruders in the literary preserve of sacred utterance. (NOTE: um, I don't think you 'are becoming'... it appears that you already ARE the greatest of intruders...) We will lose a great part of that stupendous and incomparable artistic and spiritual thing, the Gregorian chant.
...We have reason indeed for regret, reason almost for bewilderment. What can we put in the place of that language of the angels? We are giving up something of priceless worth. But why? What is more precious than these loftiest of our Church's values?
...The answer will seem banal, prosaic. (NOTE: yup, it is.)
...If the divine Latin language kept us apart from the children, from youth, from the world of labor and of affairs, if it were a dark screen, not a clear window, would it be right for us fishers of souls to maintain it as the exclusive language of prayer and religious intercourse? (NOTE: The Mass is NOT a dialogue with the world. On that supposition alone this is a very deceptive invitation.)

Moreover, the new rite of Mass establishes that the faithful are to "learn to sing 'together, in Latin, at least the parts of the Ordinary of the Mass, and especially the Creed and the Lord's Prayer, the Our Father" (n. 19). But we also remember, an admonition and a consolation, that Latin will not disappear from our Church because of this; it will remain the noble language of official acts of the Apostolic See; it will remain as a teaching instrument of ecclesiastical studies and as a key of access to the patrimony of our religious, historical, and humanistic culture, and if possible, in flourishing splendor. [My translation.]

Ma del resto il nuovo rito della Messa stabilisce che i fedeli «sappiano cantare ‘insieme, in lingua latina, almeno le parti dell’ordinario della Messa, e specialmente il simbolo della fede e la preghiera del Signore, il Padre nostro» (n. 19). Ma ricordiamolo bene, a nostro monito e a nostro conforto: non per questo il latino nella nostra Chiesa scomparirà; esso rimarrà la nobile lingua degli atti ufficiali della Sede Apostolica; resterà come strumento scolastico degli studi ecclesiastici e come chiave d’accesso al patrimonio della nostra cultura religiosa, storica ed umanistica; e, se possibile, in rifiorente splendore.

.This is absolutely not the case. ...