To be fair, if a pope uses "may not" in an encyclical, that's hardly a definitive teaching.  Not all encyclicals are infallible, by nature.  It depends how they are written.  Benedict's "openness to science" (similar to Pius XII on theistic evolution) is neither a teaching, nor a decisive statement.  In my opinion, both were horribly wrong for opening pandora's box but there is no authoritative nature in any of this.  In other words, Benedict XV was just wrong (as was Pius XII) and St Robert and company are still correct.

The Holy Office of 1633 is correct.  No, the 3rd possibility is that Benedict XV, like Pius XII, were either liberal or listened to liberal advice.  Their encyclicals were not heretical and neither were they authoritative.  When speaking on science, you can't judge such as a "teaching" in the same way as an encyclical on the sacraments.  Infallibility only protects faith/morals.  The matters of science (those discussed in the Bible) are part of Faith but also outside of it.

My opinion = they were convinced that "new facts" had emerged to possibly change the Church's views.  Theology cannot change, but science can still discover.  So since Faith and Reason are not in opposition, it is *possible* for new facts to emerge which can partially (but not substantially) change the Church's views...only in the realm of science.  That's why Benedict used "may" to denote theory and also why Pius XII said that "further investigation" is allowed on evolution.

But we know now that these "new facts" are lies and so all of this is water under the bridge.  We return to the Church Fathers and 1633 as our authority.

From Alberto Martinez' book, this paragraph from a timeline of events regarding the Galileo and Bruno affairs. 

1885 – Father William Roberts publishes his book The Pontifical Decrees Against the Doctrine of the Earth’s Movement.  In this book, Fr. Roberts presents a strong case for the position that the Church’s condemnation of heliocentrism is infallible. He concludes: (1) Alexander VIII’s Speculatores was a papal act of supreme authority by which the pope, in the face of the whole Church, confirmed and approved the decrees with his Apostolic authority, and made himself responsible for their publication, that heliocentrism was false; (2) heliocentrism was false because the Church declared it a heresy, and whoever says an opinion is heresy ipso facto says that the contradictory of that opinion has been revealed by God with sufficient certainty to oblige a Catholic to accept it by an act of divine faith; and, (3) infallible teachings, even those ex-cathedra, do not generally generate any fresh obligation of faith, but protect and vindicate one that already exists.

In any case, that quote from Benedict XV pretty much does away with the argument that it's heretical to reject geocentrism. Obviously a pope can't say, in effect, "it appears geocentrism is not correct" in an encyclical, if geocentrism is a dogma of faith. It would be like a pope saying in an encyclical, "It appears there are four Persons in God." Such a thing is against the nature of the papacy.

While wondering with great awe at the God of all creation whose attributes are infinite, we may still stand back in utter amazement when we contemplate the sizes of things in our material world, this material world which is a reflection, albeit limited, of the infinite greatness of God.  Perhaps, you will find as I do, the following site to be quite amazing as an aid in that regard: https://www.htwins.net/scale2/.

Daly's article certainly favors the idea that heliocentrism was condemned for heresy and the arguments are strong. I won't list them here. The arguments against the condemnation not being infallible were less persuasive. 1. It seemed only to be against Galileo, 2. never specifically said it was heretical (although they admit it was said other places) 3. did not define a doctrine and 4 wasn't addressed to the whole Church. I'm no theologian, nor is it necessary for me to argue in detail against the parsing of words this argument rests on, but even if technically true, the conclusion drawn would be in direct contradiction to the reason for condemnation. Why condemn what isn't heretical? How can a condemnation only apply to one man and no one else and the problem be solved if he abjured? I suppose there may be technical reasons for this opinion, but they don't add up to much. The churchmen discussed the doctrines heliocentrism contradicted and errors it promoted during the trial. Obviously, from discussion within the trial, along with the Bruno Affair and arguments and condemnations against others defending heliocentrism, they considered it all intolerable, an extreme danger to the faith as well as the source of innumerable errors, like reincarnation.  This reminds me of Anne Catherine Emmerich's assessment of the false notion of cosmology would be the mother of all heresies. 

That Robertson was a liberal has no bearing whatsoever.  He concluded, after intensely detailed work, that the condemnation was infallible and Roberts believed in heliocentrism which makes his conclusion all the more plausible.

What's truly interesting is the people who suggest that heliocentrism can't be heresy. That's strange since the entire panel of popes, saints and theologians who expounded on the problems with heliocentrism at the time were extremely erudite and animated about the errors it produced and most notably for them, because it contradicted scripture.

The devil may be in the details, but along with innumerable errors, there's another good reason to abandon heliocentrism: It can't possibly have been so deeply divisive and not be a danger to one's soul.