You are not talking about something that can be softened. If, as you say, a Pope condemned Heliocentrism in an infallible way, the Pope who doubted that condemnation, was teaching or believing heresy...manifestly. Like this quote below.

Pope Benedict XV, IN PRAECLARA SUMMORUM: ...and though this earth on which we live may not be the centre of the universe as at one time was thought, it was the scene of the original happiness of our first ancestors, witness of their unhappy fall, as too of the Redemption of mankind through the Passion and Death of Jesus Christ.

Pope Benedict here, is definitely doubting an article of faith according to you.

The Heliocentric heresy is no doubt a most complicated one. It was Cardinal Bellarmine who pointed out that the heresy was AGAINST THOSE THAT HAD SPOKEN. What he meant by this was that every word of Scripture was dictated by the Holy Ghost, no MATTER WHAT THE SUBJECT WAS, and to deny the truth of that subject matter, one that was held by all the Fathers and Tradition since the Church was founded, was the HERESY. He compared this denial of a moving sun to denying THE VIRGIN BIRTH OF CHRIST, for only in the Scriptures is this physical possibility revealed.
   
Thus to contradict the revelations in Scripture of a moving sun was to deny the word of God. This is probably one of the most interesting aspects of the whole Galileo case. Once it was believed the Church of 1616 got it wrong ON THE SUBJECT MATTER, Catholic exegesis and hermeneutics was forced to TOTALLY CHANGE WITHIN THE CATHOLIC CHURCH. 
    
First of all the 'infallibility' of the 1616 decree (then called the 'irreversibility' of the decrees) was DENIED by thousands of churchmen, theologians and philosophers, BUT NOT BY ONE SINGLE POPE. This is PROOF that the Good Lord will not allow popes to officially deny what a previous pope has decreed infallibly. In 1820 the Holy Office had to face this dilemma, an 'irreversible' dercree that was THOUGHT to be an error on the basis of scientific assertions. But by sheer genius, the Holy Office managed to have their Catholic cake (irreversible decree) and eat it (allow a new type of heliocentrism). The removal of all books advocating advocating heresy from the Index means nothing, as Pope Paul VI removed the INDEX ALTOGETHER but every heresy in them remains heresy.

As regards the REFORMATION of CATHOLIC EXEGESIS AND HERMENEUTICs, well in order to make the 1616 decree look INSIGNIFICANT they undid St Robert Bellarmine's hermeneutics and said that the 1616 decree was a matter of science (the subject matter) and that no scientific matter or matter of natural philosophy was here TAUGHT by the Holy Ghost. The whole credibility of the Catholic Church as a divinely guided religion DEPENDED NOW ON DENYING IN PUBLIC THAT THE 1616 DECREE WAS BACKED UP IN ANY WAY BY DIVINE GUIDANCE. Now with popes HAVING to go along with this REFORMATION, in order to save the Church from a 1616 decree they believed was proven false, endless contradictions came into being and Biblical understanding came under attack from all quarters from HUMAN REASONING. Accordingly Pope Leo XIII brought out the first encyclical on how the Bible should be understood and read in 1893. In it he allowed changes to some interpretations in LINE WITH THE FINDINGS OF MODERN SCIENCE. So the reformation continued. Now if we bring this to a natural conclusion, you cannot feed five thousand on five loaves of bread and two fishes, can you, so who can deny there was a caravan of bread and fishes nearby and that is what fed them. No miracle there, is there? Or is it a matter of faith God did it with five loaves and two fishes?

In 1920 Pope Benedict XV of course had to write another encyclical on biblical reading because of the CHAOS of Catholic exegesis. In it he said EVERY WORD OF THE BIBLE IS TRUE. Now we had a situation where every word of the bible is true, yet, according to Galileo's reformation, only supernatural things need be believed as revealed or taught or true. This was a great encyclical, but how can one pope 'CORRECT' a previous pope's encyclical? As for his 'MAY NOT BE THE CENTER OF THE WORLD' in his Dante Letter, well he was a victim of Einsteinianism that allowed heliocentrism and geocentrism. So Poper Benedict XV was NOT DENYING THE 1616 DECREE OR GEOCENTRISM, merely giving the opinion of science at the time. 

So on went the reinterpreting according to modern science. Finally Pope Pius XII in 1943 opened the Bible up to Big Bang theistic evolution. Now the Bible is little more than a story-book as regards all the natural philosophy and facts in it that we are told is the word of God that cannot be used to support anything in nature today.
  

I thought this was an interesting observation , at Fatima THE BLESSED MOTHER had the sun come hurtling down toward the Earth. Why not have the Earth hurtle toward the sun ? A mystery we'll find out someday.

Indeed, Finocchiaro's sizeable book is a great source of docuмentation.  That said, it is interesting to note a rather cogent comment of Dr. Robert Sungenis concerning this book.  It may be seen as a word to the wise before one proceeds in reading the book.

While admitting that Finocchiaro is a respected Galileo historian Sungenis states that Finocchiaro,  "admits in the opening pages of his latest work [Retrying Galileo] that he is driven to uncover every detail of the Galileo affair because, as he says, 'a key recurring question has been whether, how, and why the condemnation was right or wrong, and that is what the title Retrying Galileo is meant to convey.' Finocchiaro believes the Church was sincerely wrong. Hence, his motivation for 'retrying' Galileo is too find the 'real' reason the Church took such a strong stance, since he can’t believe the Church could be so obtuse to science." [my emphasis]

Yes KlasG4e, Finocchiaro is a heliocentrist who thinks the Church was wrong. Many of his comments are those of the Toms, Dicks and Harrys I spoke about that the Church allowed to decide the authority of the decrees against biblical heliocentrism.
But his history is
excellent, with no bias or favour, and he tells it as it really happened. Only for him the ignorance about the Galileo case would still be a mixture of fact and fiction it has been for hundreds of years.

Indeed, Finocchiaro's sizeable book is a great source of docuмentation.  That said, it is interesting to note a rather cogent comment of Dr. Robert Sungenis concerning this book.  It may be seen as a word to the wise before one proceeds in reading the book.

While admitting that Finocchiaro is a respected Galileo historian Sungenis states that Finocchiaro,  "admits in the opening pages of his latest work [Retrying Galileo] that he is driven to uncover every detail of the Galileo affair because, as he says, 'a key recurring question has been whether, how, and why the condemnation was right or wrong, and that is what the title Retrying Galileo is meant to convey.' Finocchiaro believes the Church was sincerely wrong. Hence, his motivation for 'retrying' Galileo is too find the 'real' reason the Church took such a strong stance, since he can’t believe the Church could be so obtuse to science." [my emphasis]

I am not sure who Finocchiaro is but he is correct  as the 'real' reason Galileo was condemned ( at least in 1633) is his concept of Quantum/Atom physics-- not astronomy. See my article The Real Galileo at  firstjesuits.wordpress.com

I thought this was an interesting observation, at Fatima THE BLESSED MOTHER had the sun come hurtling down toward the Earth.

Why not have the Earth hurtle toward the sun? A mystery we'll find out someday.

.
If the earth had done the moving, then everyone all around the globe would have noticed, but only those at Fatima noticed.
The miracle was for those who came to the Cova da Iria, not for those who did not come.
Scripture says the earth "shall not be moved," so Our Lady wouldn't want the atheists to say the Bible was wrong.
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Might have to do with the end of the world, which seemed to be happening then, but did not.
Scripture says the heavens will be rolled up like a scroll and the stars will lose their regular motion.
Most of the eye witnesses were convinced on the spot that the world was ending right there.
They fell to their knees and began to confess their sins out loud.
Atheists were converted.
The blind, sick and deaf were cured.
Everyone's clothes became dry and freshly laundered.
The muddy soil was suddenly dry.
People's shoes that had been stuck in the mud were clean, and resting normally on dry soil.
.
From a scientific perspective none of it makes any sense.
People's shoes should have been stuck in dried dirt, and they'd have to dig them out.
Dry clothes, maybe, but laundered and fresh? Impossible! Tell that to the eye witnesses.
Physically, the energy required to dry all those clothes and remove the moisture from the mud would have cooked the people.
Everyone would have died instantly, from a purely physical and normal drying by the sun's heat.
How the sun could have appeared as it did, moving that way, is entirely outside the possibility of nature.
Totally unbelievable.
Unquestionably the greatest physical miracle in modern times.
Comparable to the parting of the Red Sea or the 10 plagues of Egypt or the fire that erupted from the Temple reconstruction.
It was given "so that all may believe," but even to this day 100 years later, there are doubters.

E & S are BOTH in motion....

Yet, you Geocentrists tell me that "earth shall not be moved" means the earth is not rotating and not orbiting the Sun.
Whereas the word "shaken" or "trembling" makes a lot of sense in these verses.  
Why is there any mention of "foundations" when talking about the earth?  And "pillars"?  
The Bible is so unscientific and like a caveman, when it comes to astronomy,

Actually, I don't think the Bible says anything about Astronomy (earth rotating or orbiting).
It says "shall not be moved" and "by trembling shall be moved" and at the presence of God
"shall be moved".  It is talking about trembling and shaking and crumbling of the foundations.
This is not Astronomy.  This is Geography or Geophysics (earthquakes, tremors, etc.)