I would suggest that we can best love God with our mind in this situation by allowing what we think we have learned from the book of nature to inform our interpretation of the book of revealed Truth in Scripture. We are modifying our interpretation of the Truth to change based on current science. But note carefully that we are not changing the Truth itself, only our interpretation of it. And we only do even that after we have found no reason from Scripture itself not to, and no reason from science itself not to.
I think this is generally sound advice, although his reason for it, "Can we bear the thought of having made it more difficult for an unbeliever to come to know the richness of God’s grace toward us by our pride and stiff-neck? The idea flushes me with shame and regret," may be a bit overstated, as I don't believe accomodating modern thinking just because others will take offense otherwise is a sound practice. I doubt any dispute over doctrine or science is more of a turn off for people than the Gospel message itself.
Zimmer uses heliocentrism as his example, perhaps because of the Church's well-known failure to deal with it properly in the early 17th century. Ironically, a closer, more historically accurate look at how the Church actually did deal with heliocentrism and Galileo shows that their approach was identical to Zimmer's. To quote Philip J. Sampson in 6 Modern Myths about Christianity & Western Civilization, pp. 36-38,
The fact is that during Galileo's lifetime there was insufficient evidence to show that the earth revolves. This is now widely accepted by scholars, some even suggesting that the then-known facts weighed heavily against Galileo.
Far from being constantly harried by obscurantist priests , he was feted by cardinals, received by Pope Paul V and befriended by the future Pope Urban VIII who, in 1620, wrote an ode in his honor. The historian Georgio de Santillana observed in 1958 that "it has been known for a long time that a major part of the Church intellectuals were on the side of Galileo, while the clearest opposition to him came from secular circles." Although scholars may long have known this, the orthodox story assumes the opposite. When it is said that Galileo became "too advanced for the church," the case is rather overstated.
Robert Cardinal Bellarmine was appointed [by the Church] to examine Galileo's teachings. A distinguished scholar, he was far from ill-informed and he was told that Galileo needed to produce more evidence to establish his case; this, as we have seen, was precisely what he could not do because at the time it did not exist. Galileo was not condemned, but the church did take a harder look at Copernicus's book. It was suspended for four years in 1616 "pending correction" and reissued with several changes, largely to make it clear that the heliocentric model is only a hypothesis. Galileo was not mentioned. How, then, did things go so wrong for him?
The Church's response to Galileo is often put down to "a fear of discussion and debate," but that is not so. Alternative astronomical hypotheses were freely discussed, including Copernicus's astronomy, which, as Bellarmine remarked (in a letter to Paolo Foscarini, April 12, 1615), made "excellent good sense" as a hypothesis.
Galileo was not content with this. In order to show that the earth revolves, he advanced an ingenious but erroneous theory of the tides, and in order to defend the Copernican picture of heavenly spheres, he argued that comets were a form of optical illusion. These views put Galileo out on a limb.
He went further than this, however. He sought to reinterpret certain disputed biblical passages in the light of Copernican reasoning and in contradiction of earlier authorities. This was contrary to the Council of Trent's admonition (which had been intended for the Reformers) forbidding the interpretation of Scripture against the authority of tradition. But perhaps just as significantly, Galileo alienated his friend Pope Urban VIII.
The dispute between the Church and Galileo was due to his increasingly rude denunciations of anyone who disagreed with him rather than any doctrinal dispute over his new theories. His strongest opponents were not the Church leadership, but his fellow natural philosophers, who had a low view of his theories.
In other words, despite the Church's accomodation to this new theory, in the face of ridicule from the natural philosophers, the history we now learn in school accuses the Church of foolish pride and a stiff-neck. Accomodating sciences will do little to make the Church more acceptable to those who regard the Gospel as foolishness.
Update: I fixed some transcription errors in the quote from Sampson's book, and also put in the page numbers.
New Posts: More on Faith and Science above. More on Galileo, including some quotes from another source, here.