A common falsehood.

Yes, I meant what I wrote. I mostly agree with what you said about Pius XII and what he was and was not cautious about. However, I am pretty sure that he deliberately left room for polygenism to be accepted in the future by saying that it wasn't clear how a reconciliation would be possible, rather than by saying that a reconciliation simply was not possible. He was pretty careful in that statement, even deliberately leaving room for aliens (by adding the clause "on this earth," because if "man" is understood as "rational animal," the existence of aliens would be the existence of other men.)

People saw this even at the time and started to speculate about how "reconcilations" would be possible. While still not accepting an opinion that polygenism is definitely true, Paul VI made clear that Catholics are permitted to think that way:

"In the attempt to rethink the Theology of original sin in the light of the scientific theory of evolution and polygenism, scholars have sought to determine the literary genre of the first chapters of Genesis, and in particular Gen. 1-3. And usually, following closely the documents of the Magisterium, they affirm that it is a theological aetiology, that is, a particular vision of history, a picturesque story which is largely symbolic, of an event which really happened (original sin). Consequently, they think that the bible is not concerned with the scientific question of evolution or polygenism and these are, therefore, not denied by Revelation."

"Working on these premises, various hypotheses have been proposed to reconcile Revelation with science within the framework of a more modern theology of original sin. They are still only hypotheses, plausible to a greater or lesser extent, while the scientific theories are by no means certain and are in need of further completion and proof. The Magisterium of the Church in her latest documents has given clarifications of a specifically theological nature, while allowing those who are properly qualified to continue their studies."

Link. This may be a bit "grudging," as you described it, but it certainly does not forbid Catholics from thinking that polygenism is likely, and this was already in 1968.

This is from number 70 of Communion and Stewardship:

"With respect to the immediate creation of the human soul, Catholic theology affirms that particular actions of God bring about effects that transcend the capacity of created causes acting according to their natures. The appeal to divine causality to account for genuinely causal as distinct from merely explanatory gaps does not insert divine agency to fill in the “gaps” in human scientific understanding (thus giving rise to the so-called "God of the gaps”). The structures of the world can be seen as open to non-disruptive divine action in directly causing events in the world. Catholic theology affirms that that the emergence of the first members of the human species (whether as individuals or in populations) represents an event that is not susceptible of a purely natural explanation and which can appropriately be attributed to divine intervention."

(The idea here is that if human beings have a spiritual and immortal soul which other animals do not, the creation of that soul requires God's work; they are not saying that the physical development of humanity requires some special intervention.) In any case, "whether as individuals or in populations" basically refers to monogenism and polygenism, and the implication is that theology does not determine anything about this.

Lastly, obviously many Catholics think that polygenism is true and have said so in public works, and there has been no rebuke of this position at any time after Paul VI (as far as I know.)