That is not an accurate reading of the motu proprio. I'm sure it is one of the questions that will be answered by the Ecclesia Dei Commission. The text of the document only says that no private Masses, in either ordinary or extraordinary form, may occur during the Easter Triduum. That has always been the case. It says nothing to the effect that the traditional Triduum cannot be offered. And certainly at those parishes or chapels where only the extraordinary Mass is offered, the traditional Triduum can take place.
It is possible to do a very reverent Novus Ordo Mass in Latin, during the Triduum. Be patient!
BTW - I stumbled upon my old missals the other day and showed them to my pastor, to read the prayers for the Jews on Good Friday. In the 1959 version, the prayer begins with "Let us pray for the faithless Jews .... " By 1970, however, the prayer is drasticaly altered to reflect a more brotherly understanding and approach.
As Roy Schoeman, a Jewish convert, often points out ...
Romans 11 - “God cast a veil over the eyes of the Jews so they would not recognize Jesus until the full number of the Gentiles come into the church and then they will raise the veil from the eyes of the Jews, and they, too, will accept Christ.”
Art. 2. In Masses celebrated without the people, any priest of Latin rite, whether secular or religious, can use the Roman Missal published by Pope Blessed John XXIII in 1962 or the Roman Missal promulgated by the Supreme Pontiff Paul VI in 1970, on any day except in the Sacred Triduum. For celebration in accordance with one or the other Missal, a priest does not require any permission, neither from the Apostolic See nor his own Ordinary.
ORIGINAL: Art. 2. In Missis sine populo celebratis, quilibet sacerdos catholicus ritus latini, sive saecularis sive religiosus, uti potest aut Missali Romano a beato Papa Ioanne XXIII anno 1962 edito, aut Missali Romano a Summo Pontifice Paulo VI anno 1970 promulgato, et quidem qualibet die, excepto Triduo Sacro. Ad talem celebrationem secundum unum alterumve Missale, sacerdos nulla eget licentia, nec Sedis Apostolicae nec Ordinarii sui.
If that article is read carefully, I think you will see that what is forbidden is a priest offering a PRIVATE Mass - using either Missal - during the Sacred [Paschal] Triduum, a prohibition which is not new.
In other words, all Masses during the Sacred Triduum, using whichever Missal, must be public Masses, scheduled Masses.
I have attended parishes where two completely parallel Triduums were celebrated - one in English, one in Spanish - at different times, obviously; and one parish which was being used by a temporarily homeless Ruthenian (Eastern Rite) parish, who celebrated all (or almost all) of their many Holy Week/Triduum liturgies around our (Roman Rite) far fewer services.
At the very least, it would seem to be possible for one parish to be designated for the "Sacred Triduum according to the Missal of Blessed John XXIII."
But I don't think there is any intention in the Motu Proprio to pick the three most sacred days of the liturgical year on which to restrict a Rite that Pope Benedict clearly intends to be universally available! I think that would be completely contrary to the spirit with which the Pope has approached this matter.
Tax-man is certainly correct. It just refers to private masses being prohibited on those days.
You might do your priest a favor and clear up his confusion.