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1962 Mass is valid and Catholic, as long as the priest is validly ordained. The 1962 Mass is even licit because adding the St. Joseph prayer didn't change the essence of the the Mass. Quo Primum allows small changes to the Mass, but it outlaws anything that makes substantial changes to, or replaces, the Tridentine Mass in the Latin Rite. Notwithstanding John XXIII adding St. Joseph to the Canon of the 1962 Missal was an act of false piety to trick the Church into accepting future massive changes and, ultimately, replacement of the true Mass with the Novus Ordo sacrilege, the St. Joseph addition, per se, doesn't make the 1962 Mass illicit nor invalid.

Your entire conceptual presentation of the typical 1962 Missal as an organic emendation of Quo Primum is a fantasy....This Missal and breviary were published in a general form in the Motu Proprio, Rubricarum Instructum, on July 25, 1962.
http://w2.vatican.va/content/john-xxiii/la/motu_proprio/docuмents/hf_j-xxiii_motu-proprio_19600725_rubricarum-instructum.html

There is no mention of Quo Priumum in this docuмent.

There isn't a mention of Quo Primum (specifically) because when you revise a law which has already been revised multiple times, you don't mention the ORIGINAL law, you mention the MOST RECENT edit of the law.  The original law of Quo Primum of the 1570s was edited/replaced by Pope St Pius V himself.  So it lasted a few years at most.  Then came Pope Clement VIII's revisions, Pope Urban VIII's revisions, Pope Leo XIII's revisions, Pope St Pius X's revisions, Pius XII's edit of Holy Week and then John XXIII's revisions - which specifically mentions the laws of St Pius X and Pius XII, because these were the CURRENT laws IN EFFECT in 1961.

St Pius X's law doesn't mention Quo Primum either (because that law was replaced by St Pius V himself), but he does mention St Pius V and all the popes who made revisions after St Pius V, because these are all "legal links" in the "chain" of St Pius V's liturgy.   John XXIII's law only mentions St Pius X's law, because up until 1961, Pius X's missal and Pius XII's changes to the Holy Week liturgy were the LAW of the roman rite.  St Pius X's missal (up until John XXIII's changes) was = Quo Primum, in legal terms, because it was the current MISSAL of Quo Primum.  What matters is the question:  What rite/missal is legally binding on the whole Latin Church?  Pope John XXIII's law makes this clear, that it's his that is binding (which I will show, in detail).

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But first, let's look at the legal language of St Pius X's changes, so we can compare them to John XXIII's legal language.

Pius X's law "Divino Afflatu" of 1911 - A revision of the Breviary   (https://breviary.net/divino-afflatu.htm)

(Referencing the linked docuмent above, 3rd paragraph):
With good reason was provision made long ago, by decrees of the Roman Pontiffs, by canons of the councils, and by monastic laws, that members of both branches of the clergy should chant or recite the entire psaltery every week. And this same law, handed down from antiquity, our predecessors St. Pius V, Clement VIII and Urban VIII religiously observed in revising the Roman breviary. Even at present the psaltery should be recited in its entirety within the week were it not that owing to the changed condition of things such recitation is frequently hindered.

(7th-9th Paragraphs)
Therefore, by the authority of these letters, we first of all abolish the order of the psaltery as it is at present in the Roman breviary, and we absolutely forbid the use of it after the 1st day of January of the year 1913. From that day in all the churches of secular and regular clergy, in the monasteries, orders, congregations and institutes of religious, by all and several who by office or custom recite the canonical hours according to the Roman breviary issued by St. Pius V and revised by Clement VIII, Urban VIII and Leo XIII, we order the religious observance of the new arrangement of the psaltery in the form in which we have approved it and decreed its publication by the Vatican printing press. At the same time we proclaim the penalties prescribed in law against all who fail in their office of reciting the canonical hours everyday; all such are to know that they will not be satisfying this grave duty unless they use this our disposition of the psaltery.

We command, therefore, all the patriarchs, archbishops, bishops, abbots and other prelates of the church, not excepting even the cardinal archpriests of the patriarchal basilicas of the city, to take care to introduce at the appointed time into their respective dioceses, churches or monasteries, the psaltery with the rules and rubrics as arranged by us; and the psaltery and these rules and rubrics we order to be also inviolately used and observed by all others who are under the obligation of reciting or chanting the canonical hours. In the meanwhile it shall be lawful for everybody and for the chapters themselves, provided the majority of the chapter be in favor, to use duly the new order of the psaltery immediately after its publication.

This we publish, declare, sanction, decreeing that these our letters always are and shall be valid and effective, notwithstanding apostolic constitutions and ordinances, general and special, and everything else whatsoever to the contrary. Wherefore, let nobody infringe or temerariously oppose this page of our abolition, revocation, permission, ordinance, precept, statue, indult, mandate and will. But if anybody shall presume to attempt this let him know that he will incur the indignation of almighty God and of his apostles the blessed Peter and Paul.

Given at Rome at St. Peter’s in the year of the incarnation of our Lord 1911, on November the first, the feast of All Saints, in the ninth year of our pontificate.


Summary:  St Pius X's law tells us 1) the current law in force is abolished, 2) his new law must be used, 3) who must follow the law, 4) when it takes effect, 5) the penalties for not obeying.

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Now let's look at Pius XII's changes to Holy Week.

Pius XII's law - "Maxima Redemptionis Nostrae Mysteria"  https://www.catholicculture.org/culture/library/view.cfm?recnum=11136 

(9th Paragraph)
The Most Eminent Fathers, assembled in extraordinary congregation at the Vatican Palace on July 19, 1955, after mature deliberation, recommended by unanimous vote that the restored Order of Holy Week should be approved and prescribed, if it should please His Holiness.
 
When all these matters had been individually reported to the Holy Father by the undersigned Cardinal Prefect, His Holiness deigned to approve the recommendations of the Most Eminent Cardinals.  Wherefore, by special mandate of our Most Holy Lord, Pius XII, by divine Providence Pope, the Sacred Congregation of Rites has decreed the following:

I. The restored Order of Holy Week is prescribed
1. Those who follow the Roman rite are bound to observe in the future the restored Order of Holy Week, as described in the typical Vatican edition. Those who follow other Latin rites are bound to observe only the time set in the new Order for the liturgical functions.
2. This new Order must be observed from March 25, 1956, the Second Passion Sunday, or Palm Sunday.
3. No commemoration is allowed during the entire Holy Week, and collects commanded under any title are prohibited at Mass.
II. The proper hour for the celebration of the sacred Liturgy in Holy Week

etc, etc, etc.  It's a very long docuмent, which makes many minor changes to the breviary, missal and Holy Week rites, but it is the law and all in the Roman Rite must follow.

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Now let's look at John XXIII's law to see the similarities in language.

John XXIII's law - "Rubricarum Instructum"   http://sanctaliturgia.blogspot.com/2005/11/rubricarum-instructum-english.html

(2nd paragraph)
Hemce, it is not surprising that our Predecessor Pope Pius XII, of happy memory, acceding to the wishes of many of the bishops, should have judged it expedient to reduce the rubrics of the Roman breviary and missal to a simpler form in certain respects. This simplification was enacted by a decree of the Sacred Congregation of Rites dated March 23, 1955.

(5th - 8th paragraphs)
We ourselves, therefore, of our own accord [motu proprio] and with full knowledge, have seen fit to approve by our apostolic authority the body of these rubrics of the Roman breviary and missal prepared by the experts of the Sacred Congregation of Rites and carefully revised by the aforesaid pontifical commission for general liturgical reform. And we decree as follows:

1. We command that, beginning on the first day of January of next year, 1961, all those who follow the Roman rite shall observe the new code of rubrics of the Roman breviary and missal arranged under three headings - "Genreal Rubrics," "General Rubrics of the Roman Breviary," and "General Rubrics of the Roman Missal" - to be published shortly by our Sacred Congregation of Rites. As for those who observe some other Latin rite, they are bound to conform as soon as possible both to the new code of rubrics and to the calendar, in all those things which are not strictly proper to their own rite.

2. On the same day, Janurary 1, 1961, the "General Rubrics" of the Roman breviary and missal, as well as the "Additions and Variations" to the rubrics of the Roman breviary and missal according to the bull Divino afflatu of our predecessor St. Pius X, which have hitherto been prefixed to these books, shall become inoperative. As the provisions of the decree, The Reduction of the Rubrics to a Simpler Form , dated March 23, 1955, have been incorporated into this new edition of the rubrics, this general decree of the Sacred Congregation of Rites shall likewise become inoperative. Finally, any decrees and replies on doubtful points issued by the same Congregation which do not agree with this new form of rubrics shall be abrograted.

3. Likewise, statues, priveleges, indults, and customs of any kind whatsoever, including those that are centenary and immemorial, even if they are worthy of special and individual mention, shall be revoked if they are opposed to these rubrics.



-----Comments:  Pope John XIII issued a new missal/breviary, he said that the old missal/breviary of St Pius X was inoperative (i.e. cannot be used) and he said that Pius XII's law of 1955 was also inoperative (because Pius XII's Holy Week changes were included in John XXIII's new missal).  Then he said, lastly, that any other decrees which disagree with his new missal are "abrogated" (which means stopped, overturned, repealed).  Pope John is VERY clear that every missal/breviary change BEFORE his missal is now illegal.  His missal is now to be used and only used. 

Let us also note that Quo Primum was not revoked.  The 1962 missal of Pope John is a REVISION of Pius X's missal, which is a revision of Pope Leo XIII, etc, etc all the way back to Pope St Pius V.  All these popes who made revisions to Quo Primum were not revising the SUBSTANCE of the missal, but only the RUBRICS.  The rubrics are part of the missal but do not change the ESSENCE of the mass.  The rubrics govern the where, how, when you say the breviary/mass but do not change the substance of the breviary/mass itself. 

Every change made by Clement, Urban, Leo, Pius X, Pius XII and John XXIII to St Pius V's law of Quo Primum were accidental changes, rubrical changes and non-essential changes.  Quo Primum's commands, permissions, authorizations and allowances relating to the Roman Rite were both rubrical AND doctrinal/theological.  The rubrics can be changed/updated over the course of time, while the doctrinal/theology of the mass can never be changed and was codified "in perpetuity".  No pope to date has attempted to change the essense of the mass of Pius V, who was passing along the essence of the mass which Pope St Gregory the Great formulated, who he received from the Apostles themselves.

Paul VI did not attempt to change the essence of the latin rite (for he knew he could not); he attempted to issue a new rite and have the latin church accept it voluntarily.  But that's another topic...

What is worse for your argument, the first typical edition of the 1962 Missal was first published in July 25, 1962.  St. Joseph’s name was not added to the communicantes until December 8, 1962 by John XXIII in Nove hisce temporibus.

So just what is the “typical edition” of the 1962 Missal?  I do not know and neither do you, and a lot of people who are very knowledgeable about this question have not arrived at any definitive answer either.

I can't find the docuмent you reference which has an english translation of the addition of St Joseph.  If this addition wasn't part of the original July 25 law, then my argument is STRONGER, because it means that this addition is not part of "legal chain" which links to back to Quo Primum.  If the addition of St Joseph was an "extra" change by John XXIII, and does not carry the same legal obligations or command to use it (similar to the way the 65/69 changes were not obligatory) then such a change is optional and not binding under pain of sin.

Every law must state its purpose, its limits, its audience and its penalities for disobedience.  Unless I can read the docuмent, I don't know these facts related to this issue.

The "typical edition" would have to be understood as what was published on July 25, 1962.  All additional changes were made as part of V2 reforms (and EVERY V2 reform is optional on the conscience of all catholics).