Stubborn, Magisterium simply means, Teaching Authority. For e.g. Pope Pius XII in Humani Generis uses Pope Pius XII speaks of the Ordinary Magisterium, the Ordinary Teaching Authority, "these matters are taught with the ordinary teaching authority" (p.20)
In the citation you provide from Pope Bl. Pius IX, "the ordinary teaching authority of the entire Church spread over the whole world", is a reference to the Ordinary and Universal Teaching Authority of the Church. Notice that the criterion of universality given by Pope Pius IX is that it is that of the Church spread over the whole world, that is what universality in Ordinary and Universal Magisterium means.
Another example from Van Noort, cited by Salza and Siscoe: ""Meantime, notice that the Church possesses infallibility not only when she is defining some matters in solemn fashion, but also when she is exercising the full weight of her authority through her ordinary and universal teaching. Consequently, we must hold with an absolute assent, which we call ‘ecclesiastical faith,’ the following theological truths: (a) those which the Magisterium has infallibly defined in solemn fashion; (b)
those which the ordinary magisterium dispersed throughout the world unmistakably proposes to its members as something to be held (tenendas). So, for example, one must give an absolute assent to the proposition: ‘Pius XII is [present tense] the legitimate successor of St. Peter’; similarly … one must give an absolute assent to the proposition: ‘Pius XII possesses the primacy of jurisdiction over the entire Church.’ For — skipping the question of how it begins to be proven infallibly for the first time that this individual was legitimately elected to take St. Peter’s place — when someone has been constantly acting as Pope and has theoretically and practically been recognized as such by the bishops and by the universal Church, it is clear that the ordinary and universal magisterium is giving an utterly clear-cut witness to the legitimacy of his succession." (Sources of Revelation, p. 265)
http://www.trueorfalsepope.com/p/peaceful-and-universal-acceptance-of.htmlAfter we identify the OUM, the next stage is to observe (1) it is impossible that it has collectively defected into heresy or apostasy. (2) it is impossible that all members of the episcopal college have died without replacement. The implications of this for (1) the validity of the new rite (2) the SV question etc, can then be more closely studied.
Ladislaus claims, "Right now, since the Holy See is vacant, the OUM is not being exercised.", but that begs the question. The Conclusion is assumed in the Premise. Rather, since the OUM teaches that the Holy See is occupied, it follows as infallibly true that in fact it is.
See this book:
https://archive.org/details/outlinesofdogmat01hunt/page/n6 " ... it affords an answer to a much vaunted objection to the claims of the Catholic Church, put forward by writers who think that they find proof in history that the election of a certain Pope was simoniacal and invalid, and that the successor was elected by Cardinals who owed their own appointment to the simoniacal intruder; from which it is gathered that the Papacy has been vacant ever since that time. A volume might be occupied if we attempted to expose all the frailness of the argument which is supposed to lead to this startling conclusion; but it is enough to say that if the Bishops agree in recognizing a certain man as Pope, they are certainly right, for otherwise the body of the Bishops would be separated from their head, and the Divine Constitution of the Church would be ruined." See also the citation from Van Noort by Salza and Siscoe on their website.
The Teaching Church's Indefectibility prevents it from wrongly recognizing its Head. If we could agree on that, we could study the other implications of Indefectibility. SV's raise various objections to R&R, and R&R raise various objections to SVism.
Neither position holds the complete truth. R&R is closer, in so far as it at least recognizes an OUM. But saying the entire OUM of the Church today can collectively fall into heresy, just so long as all the Bishops who exercise the OUM do not die, the as some (not all) R&R do, is also mistaken. A careful study of these things will show R&R needs slight modification.