This is a useful post. Thanks.
I think I have realised something. You and I aren't entirely arguing about the same thing.
I don't deny for a second that members of the church were engaged in scientific things around the time of Galileo, as well as before and afterwards. And indeed, I wouldn't deny that the Church was the key repository of education in the Middle Ages when almost no one else was in that business in the Latin West.
But that's a different thing from saying (i) that the Church also destroyed all sorts of things it didn't like, (ii) that it sought to frustrate lines of enquiry which challenged its authority and (iii) that this resulted in the build up of all sorts of pressures (and these developed into things like the Reformation and the argument with a science free of a religious preference).
And of course, it's a long period of history in which lots of things were happening.
Here's a picture of what I think broadly fills the gap between Nicaea and Galileo - it is the encroachment of an absolutist idea of Rome's authority and the reaction to this which necessarily causes schisms with those Rome sought authority over.
The Council of Nicaea is a reasonable starting point. It is when Constantine raised the Church up and put it on the path to its ascendancy. It is when the justification of a dogmatic idea of Christian religion was given its form. As I wrote earlier, people are at their most dangerous when they feel an inviolable sense of self-righteousness. The claim of high virtue has justified much of the worst evil in human history. Religion has the ability to generate this behaviour (but it is not the only source for it).
From the Council of Nicaea when Constantine was emperor, to the end of Justinian's rule, the destruction of pagan culture was vast, savage and deliberate. Some of the destruction was done by Germanic tribes. But an enormous amount was also done by emperors, bishops and mobs. Nearly every element of imperial pagan culture was destroyed in this 250 year period. One of Constantine's first actions as a "Christian" emperor was to sack the Oracle of Apollo at Dydima and torture the pagan priests to death. During the remainder of the early imperial Christian period, amongst other things, the Serapeum library in Alexandria was destroyed, the Neo-Platonic school in Athens was closed, Hypatia was murdered, Jovian ordered the destruction of the library at Antioch, the Mysteries of Samothrace were closed down, the Olympic Games were stopped and non-Christians were called by the emperor Theodosius “loathsome, heretics, stupid and blind”. This is a small sample of a large enterprise.
The entire progress of classical science and literature almost disappeared during this period not to be seen again for a thousand years. There is the odd exception - in which a person like Isidore of Seville or the venerable Bede pops up. But it is pretty clear that any ancient works that survived were confined within libraries to which only ecclesiastical folks had access. And the ideas which emerged from the church conformed with church doctrine. The anathemas, index and institutions of the church also required it.
When the Western empire fell, the Pope emerged from the barbarian destruction as a powerful figure. The papacy was a political organism seeking to expand its authority and to restrain competing interests. A famous document (and convenient forgery), the Donation of Constantine, made the Pope's claim explicit. It granted the Pope "power, and dignity of glory, and vigour, and honour imperial [and] supremacy as well over the four principal sees, Alexandria, Antioch, Jerusalem, and Constantinople, as also over all the churches of God in the whole earth."
The theology the church promoted was entirely consistent with its politics. It was a theology in which Rome asserted control over all of Christendom. This led in time to the theological schism with Eastern orthodoxy.
So what you are seeing in the intellectual argument is a papal apparatus designed to build a theological shell around a political claim. You see the same kind of argument with competing ideas in theology as you do in science later on. One that bears some resemblance - as an argument over authority - is the dispute between the pope and the Byzantine Patriarch Photius.
This claim to authority rankled, of course, with those over whom the Roman church claimed dominion.
"My dearest brother, we do not deny to the Roman Church the primacy amongst the five sister Patriarchates; and we recognize her right to the most honourable seat at an Ecumenical Council. But she has separated herself from us by her own deeds, when through pride she assumed a monarchy which does not belong to her office." - Nicetas, Archbishop of Nicomedia in the twelfth century.
She assumed a monarchy which does not belong to her office.
There's the issue. The church imposed its monarchy on science as well. It was, of course, delighted by the science of confirmation. It wasn't so delighted by a science of refutation, in which the church lost control of the debate. In which folks argued things of which the church didn't approve. In which ideas didn't conform with the notion of papal authority and intercession between the temporal and spiritual worlds.
Really, the beginning of the end was the wave of classical knowledge that was retrieved from the Eastern empire and from Islam from the twelfth century onwards. The cat was out of the bag. At first, folks like Thomas Aquinas were able to tether the philosophies of the ancients to contemporary ideas of christian philosophy. But the new universities modelled on Islamic schools were democratising education. Throw in the printing press and technologies like the telescope and fresh minds were going to join the conversation and existing ideas were bound to be subject to review.
In a sense, the Copernican universe challenged the entire medieval church theology. And as I suggested above, the theology justified the church's politics. Galileo's argument - which said that earth was not central and that nature expressed God's creative will as well as a book - damaged the pope's claim to be the Vicar of Christ. But why should Galileo not make his argument - at least as seen using a modern lens?
As the Greek East had already said, Rome assumed a monarchy which does not belong to her office.
In the end, the church lost the monarchy which it had wrongly claimed.
ps I don't submit to the catholic argument that the issue wasn't about heliocentrism. I have provided the text of the inquistion's judgement which explicitly states the issue was Galileo's advocacy of the heresy of the Copernican model. There would be no need to bring Copernicus into the discussion other than because his model of the universe was in play.
pps I don't think one needs to be sceptical of a catholic simply because they are a catholic, but scholars come with different qualities. The article you linked was nicely written but it assumes the reasonableness of the papacy's monarchical rights over the scientific conversation. Like Nicetas, I demur.
| 
– Invented the Foucault pendulum to measure the effect of the earth's rotation