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The Church doesn't teach anything about the shape of the earth.
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The shape of the earth is not something the Church has authority to teach in the first place.
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The Church is not concerned with what the earth's shape is.
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The horizon always appears perfectly flat 360 degrees around the observer regardless of altitude. All amateur balloon, rocket, plane and drone footage show a completely flat horizon over 20+ miles high. Only NASA and other government "space agencies" show curvature in their fake CGI photos/videos.

The horizon always rises to the eye level of the observer as altitude is gained, so you never have to look down to see it. If Earth were in fact a globe, no matter how large, as you ascended the horizon would stay fixed and the observer / camera would have to tilt looking down further and further to see it.

The natural physics of water is to find and maintain its level. If Earth were a giant sphere tilted, wobbling and hurdling through infinite space then truly flat, consistently level surfaces would not exist here. But since Earth is in fact an extended flat plane, this fundamental physical property of fluids finding and remaining level is consistent with experience and common sense.

They did not want to say the earth is a globe.  It does not matter for salvation whether the earth is a globe or not.  They wanted to explain a basic principle for understanding Scripture. 
Scripture does not teach the earth is a globe.  Scripture does not teach the earth is flat.  Scripture is not intended to teach on the subject either way because it is a matter of physical science.  This is perfectly clear in the quotes I gave.  There is nothing vague about it.

Clearly they did not want to say the earth was a globe, because they knew deep down, like you, that it was false.

They are unclear, in that that we don't know what exactly they are referring to. Speaking too generally. Unclear at least for the purpose of trying to prove the globe earth like you are.

 Obviously scripture is not a science book and more than I can learn physics from my cookbook. But certain important aspects such as the sun and the moon etc. can be taken from it. If what you say is true than the Fathers who used scripture to speak of the solidity of the firmament etc. were wasting their time.

Jaynek vs Church Fathers.

I'm a convert to Catholicism.  So, I had to take RCIA classess.  One of our last lessons included a video by Bishop Barron on Faith and Reason.  I can't find the video on youtube, but basically he says what Jaynek is saying, that The Bible is like "Moby Dick."  A great fiction, with good ideas in it.  

I am not saying anything like that.  I am quoting papal encyclicals and they are not saying anything like that.  They teach, and I believe, that Scripture is without error.  Interpreted through the Church, it is an unerring guide to faith and morals.  But we should not use figures of speech like "the four corners of the earth" to determine that the earth is a square or flat or anything else about its shape because, as the Church teaches, Scripture does not intend to 
teach about the shape of the earth or anything in the realm of physical science.

I have to wonder of it's Bishop Barron who is feeding Jayne information to post here.  

Nobody "fed me information".  I used a search engine to figure out which popes taught about Scripture and then read the encyclicals they wrote.  Every time I have quoted a pope or a Saint, I have tried to locate the primary source so I could read it in context and make sure I understood it properly.

But we should not use figures of speech like "the four corners of the earth" to determine that the earth is a square or flat or anything else about its shape because, as the Church teaches, Scripture does not intend to
teach about the shape of the earth or anything in the realm of physical science.

We use both scripture and science.

So to believe that the earth is a globe, like you do, one has to have very compelling evidence.

What we see is flat.

Pope St. Pius X – Responses of the Biblical Commission

Question 3. Is it possible, in particular, to call in question the literal and historical meaning where there is question of facts narrated in these same chapters that touch the foundation of the Christian religion, such as, among others, the creation of all things that was accomplished by God at the beginning of time, the special creation of man, the formation of the first woman from the first man, the unity of the human race, the original happiness of the first parents in a state of justice, integrity, and immortality, the command given by God to man to prove his obedience, the transgression of the divine command at the instigation of the devil under the form of a serpent, the fall of the first parents from that primitive state of innocence, and the promise of a future Redeemer?

Response: No


https://thesocraticcatholic.com/2017/02/08/pope-st-pius-x-responses-of-the-biblical-commission/



I think the above is VERY interesting. If you read the link the only thing that he says we can diverge on is whether creation was a literal 7 days.

I read the link.  It supports what I am saying.

Question 7. Although it was not the intention of the sacred author, when writing the first chapter of Genesis, to teach us in a scientific manner the innermost nature of visible things and the complete order of creation but rather to hand on to his people a popular account, such as the common parlance of that age allowed, adapted to the senses and to man’s capacity, is it necessary, when interpreting these chapters, to seek strictly and always the particular characteristics of scientific discourse?


Response: No.

The question that you quoted concerned historical facts related to faith, such as " the creation of all things that was accomplished by God at the beginning of time, the special creation of man, the formation of the first woman from the first man, the unity of the human race, the original happiness of the first parents in a state of justice, integrity, and immortality, the command given by God to man to prove his obedience, the transgression of the divine command at the instigation of the devil under the form of a serpent, the fall of the first parents from that primitive state of innocence, and the promise of a future Redeemer."  

Note that there is nothing in this list about the shape of the earth or the arrangement of the cosmos.

Obviously scripture is not a science book and more than I can learn physics from my cookbook. But certain important aspects such as the sun and the moon etc. can be taken from it. If what you say is true than the Fathers who used scripture to speak of the solidity of the firmament etc. were wasting their time.

Jaynek vs Church Fathers.

Leo XIII addresses this in Providentissimus Deus (par 19)

The unshrinking defence of the Holy Scripture, however, does not require that we should equally uphold all the opinions which each of the Fathers or the more recent interpreters have put forth in explaining it; for it may be that, in commenting on passages where physical matters occur, they have sometimes expressed the ideas of their own times, and thus made statements which in these days have been abandoned as incorrect. Hence, in their interpretations, we must carefully note what they lay down as belonging to faith, or as intimately connected with faith-what they are unanimous in. For "in those things which do not come under the obligation of faith, the Saints were at liberty to hold divergent opinions, just as we ourselves are,"(55) according to the saying of St. Thomas.

Did the Fathers speak unanimously of the solidity of the firmament as a matter pertaining to faith?  No, they did not.  

People who reject the Bible for not being accurate in regards to Science are ignoring Church teaching on Scripture.  Often it is because they are looking for an excuse to avoid obeying God.
What catechism are you reading from that says Catholics should believe the earth is flat?

Scripture. Vatican I,Canons and Decrees, Chapter III: Of Faith, says:
... all those things are to be believed with divine and Catholic faith which are contained in the Word of God,, written or handed down, and which the Church, either by a solemn judgment or by her ordinary teaching (magisterium),proposes for belief as having been divinely revealed. ... ... although faith is above reason, there can never be any real discrepancy between faith and reason; since the same God Who reveals mysteries and infuses faith has bestowed the light of reason on the human mind, and God cannot deny Himself, nor can truth ever contradict truth. The false appearance of such a contradiction is mainly due, either to the dogmas of faith not having been understood and expounded according to the mind of the Church, or to the inventions of opinion having been taken for the verdicts of reason. We define, therefore, that every assertion contrary to a truth of enlightened faith is utterly false. Further, the Church, which together with the apostolic office of teaching, has received a charge to guard the deposit of faith, derives from God the right and the duty of proscribing false science, lest any should be deceived by philosophy and vain deceit (can.ii) Therefore all faithful Christians are not only forbidden to defend as legitimate conclusions of science such opinions as are known to be contrary to the doctrines of faith, especially if they have been condemned by the Church, but are altogether bound to account them as errors which put on the fallacious appearance of truth. (D1797-8)
Galileo would have us believe that there is an absolute separation in Holy Scripture between matters of faith and morals and matters pertaining to the physical sciences. That such is not at all the case, Pope Benedict XV assures us in Spiritus Paraclitus (Sept. 15, 1920):
... by these precepts and limits [set by the Fathers of the Church] the opinion of the more recent critics is not restrained, who, after introducing a distinction between the primary or religious element of Scripture, and the secondary or profane, wish, indeed, that inspiration itself pertain to all the ideas, rather even to the individual words of the Bible, but that its effects and especially immunity from error and absolute truth be contracted and narrowed to the primary or religious element. For their belief is that that only which concerns religion is intended and is taught by God in the Scriptures; but that the rest, which pertains to the profane disciplines and serves revealed doctrine as a kind of external cloak of divine truth, is only permitted and is left to the feebleness of the writer. It is not surprising then, if in physical, historical, and other similar affairs a great many things occur in the Bible, which cannot at all be reconciled with the progress of the fine arts of this age. There are those who contend that these fabrications of opinions are not in opposition to the prescriptions of our predecessor [Leo XIII] since he declared that the sacred writer in matters of nature speaks according to external appearance, surely fallacious. But how rashly, how falsely this is affirmed, is plainly evident from the very words of the Pontiff.

I read the link.  It supports what I am saying.
The question that you quoted concerned historical facts related to faith, such as " the creation of all things that was accomplished by God at the beginning of time, the special creation of man, the formation of the first woman from the first man, the unity of the human race, the original happiness of the first parents in a state of justice, integrity, and immortality, the command given by God to man to prove his obedience, the transgression of the divine command at the instigation of the devil under the form of a serpent, the fall of the first parents from that primitive state of innocence, and the promise of a future Redeemer."  

Note that there is nothing in this list about the shape of the earth or the arrangement of the cosmos.

You dishonestly left the description of the Firmament out of your list. That specifically deals with the shape and arrangement of the cosmos.