I share the view that we should look at a broader background than Unitatis Redintegratio of Vatican II, considered in isolation, if we desire a Catholic and 'Traditional' account of "Ecumenism". The following roughs out some lines of thought which I have been considering, based upon evidence. (I am not really interested in opinions which are evidentially unbased.) Please regard it as inchoate; please understand that it is intended less to assert than to ask.
The Roman See has not always treated Oriental groups seeking Full Communion as if they were merely groups of individual schismatics some of whom happened to possess technically 'valid' Orders. The Oriental bishops at Florence were, surely, treated as having real status as Patriarchs and Bishops. As late as Vatican I, dissident Oriental bishops were sent invitations to the Council*. When the Melkite Patriarchate of Antioch regularised its position with Rome in the early 18th century, I know no evidence that its hierarchy was granted jurisdiction. Benedict XIV (Demandatam caelitus) assured Cyril VI and his bishops: "We have no other intention ... but that the due obedience of your people and your authority and jurisdiction over them shall be kept whole and entire ... We wish all the rights, privileges, and free jurisdiction of Your Fraternities to remain intact". Indeed, there is evidence that, in the period before the definitive restoration of Full Communion, Jesuits working within the Patriarchate of Antioch had treated all Melkite bishops as the local Ordinaries.
Perhaps surprisingly, even the 1917 Code of Canon Law ... yes, I did say 1917 ... permitted the faithful to seek the Sacraments from an excommunicate ministers "ex qualibet iusta causa" (i.e. not necessarily even "ex gravi causa"; vide 2261 para 2). In the first part of the twentieth century, Latin theologians advanced differing interpretations of the de facto acceptance by Rome of jurisdiction (for example, to absolve) within Orthodox communities (at the end of Lumen Gentium, among the Notificationes appended by the Docrinal Commission, we find an admission that "variae exstant sententiae" among theologians "quod attinet ad potestatem quae de facto apud Orientales seiunctos exercetur".) It would be difficult to sustain a claim that, according to Catholic Tradition, ecclesiastical jurisdiction only authentically exists in full canonical unity with the See of Rome.
Perhaps the evidence is even stronger with regard to the Patriarchate of Moskow. After all, spats between Rome and Constantinople went back to the first millennium, while Rome and Moskow had always been rather more cut off from each other (did the Russian Church formally denounce the decrees of Florence in the 1480s?). The fabulously erudite Benedictine Orientalist Jean-Baptiste-Francois Pitra, Cardinal Bishop of Frascati and Archivist of the Holy Roman Church, took the view that the separation between Rome and Moskow was neither juridical nor formal; a view shared not only by the maverick Russian Orthodox lay theologian Vladimir Soloviev but also, significantly, by the great Ukrainian Greek Catholic Metropolitan Andrew Sheptytsky. Metropolitan Andrew was what the early Latin Christians called a Confessor: one who witnessed to Christ with the offer of his life but was never called to shed his blood. During the course of his heroic life, in which he saw the insides of many prisons, he was an indefatigable worker, not only for his own flock, but also for the unity of all Christians of the Byzantine Rite with the See of S Peter. He dealt with Russian Orthodox in ways that accorded ill with the views of some tidy-minded Latins. There survives a printed document copies of which he presumably handed out to Ukrainian Confessors ...
I shall deal with it, Deo volente, in a day or two's time.
*Bishop C Butler wrote "It is possible to argue, and has been argued from the Roman Catholic side, that 'schism' was never formally consummated between these two great communions".
Benedict XIV reminded us, in general terms, that we cannot definitively deny the propriety of any sacramental sharing, because the Catholic Church grants dispensations for mixed marriages ... in which, according to Western theology, the two ministers of the Sacrament belong to different communions.