The Church has the authority to decide that an opinion on science is contrary to Scripture and dangerous to the Faith. Evolution is a clear example of that. (Heliocentrism is less so since the condemnation was later lifted.) Lay people do not have the authority to make those sorts of claims.  The Church has never taught anything like that about a globe earth.

You quote Saints who drew conclusions about physical science from Scripture long before Pope Leo taught not to.  This does not cancel out his teaching so that we who know of it may ignore it.  And it is ironic that you cite St. Augustine when you ignore the principle he taught:

The flat earthers are not insisting on a literal interpretation, but a literalistic one.  

A literal interpretation is one that considers the information that the Sacred author intends to convey.  
A literalistic one takes figurative language as if it were literal.  

When a passage is about the Second Coming, for example, the literal interpretation concerns the Second Coming.  

A literalistic one finds a figure of speech in the passage, treats it as literal and deduces that the earth is flat, even though it is obvious that the author had no intention to teach about this.  

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There are many things about the phases of the moon that demonstrate how the earth's surface is spheroidal.
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For example:
-- Everywhere on the earth where the moon is visible, everyone always sees the same phase at the same time.
  There is no exception to this fact.
  But if the earth were "flat," viewers separated by a few thousand miles would always see a DIFFERENT phase.
  That NEVER happens. Therefore, the earth cannot be "flat."
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-- At the first quarter moon and the last quarter moon, at that very hour the moon makes a right triangle with the sun and earth.
  With the moon at the 90 degree corner, we can measure the angle of the earth's corner, which turns out to be 89.6 degrees.
  Since the sum of the three interior angles of any triangle is 180 degrees, that leaves 0.4 degrees for the sun's corner.
  This is a very thin and long triangle, with the earth and moon at one end and the sun at the other end.
  The sun is placed over 300 times further from earth than the moon is from the earth.
  This is impossible on a "flat" earth model, therefore the "flat" earth model is shown to be impossible.
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-- When we look up at the moon from waxing crescent to waning crescent (all except new moon) we see the following:
  The moon's illuminated side always faces the sun. Therefore we can see it's the sun that makes the moon light up.
  Flat-earthers are all in disagreement about this so they have all kinds of silly explanations, like:
  -- The moon is translucent and you can see stars shining through it
      The moon does not shine by the sun's light but is illuminated from inside (somehow but we don't know how).
      The moon is a flat disk not a globe and the phases we see have nothing to do with the sun (?).
      Since none of their silly claims ever amount to a "hill of beans" consequently flat-earthism is relegated to urban legend.
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-- The full moon at midnight is always directly overhead, from any point of view on earth. Therefore:
   We can easily imagine where the sun is located in order to make the moon look this way.
   With the moon overhead at "high noon" position in the sky, the sun must be under our feet on the other side of the earth.
   The moon, earth and sun must be in a straight line in space for us to see the moon "full" as we do in a full moon.
   -- But flat-earthers claim the sun is circling above the "flat" earth and is therefore behind our back, to the north.
       If the sun were where flat-earthers say it is, we ought to see a shadow at the bottom of the moon, not a full moon.
       Since we never see a shadow at the bottom of the moon during full moon, the earth cannot be "flat."      
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Do you need more examples?
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You scored a bullseye here, Jaynek.
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A literalistic person practices literalism while literalistcally looking for a literalist meaning in everything.
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But the Church never has and never will support literalism.
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Proper understanding of Scripture does not seek to impute literalism into everything in the Bible.
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CHAP. 5.--IT IS A WRETCHED SLAVERY WHICH TAKES THE FIGURATIVE EXPRESSIONS OF SCRIPTURE IN A LITERAL SENSE.
9.But the ambiguities of metaphorical words, about which I am next to speak, demand no ordinary care and diligence. In the first place, we must beware of taking a figurative expression literally. For the saying of the apostle applies in this case too: "The letter killeth, but the spirit giveth life."(2) For when what is said figuratively is taken as if it were said literally, it is understood in a carnal manner. And nothing is more fittingly called the death of the soul than when that in it which raises it above the brutes, the intelligence namely, is put in subjection to the flesh by a blind adherence to the letter. For he who follows the letter takes figurative words as if they were proper, and does not carry out what is indicated by a proper word into its secondary signification... Now it is surely a miserable slavery of the soul to take signs for things, and to be unable to lift the eye of the mind above what is corporeal and created, that it may drink in eternal light.

Agreed. The globers try to prove the pagan NASA globe earth as best they can. But they cannot change what God has created.

Note how strongly St. Augustine wrote when he addressed this issue in On Christian Doctrine:
– Book III, Ch. 5

Yeah, that whole "Eat my flesh and drink my blood thing is really soul killing slavery.

No Catholic should say that "eat my flesh and drink my blood" is an example of a figurative expression.  The Eucharist really is the Body and Blood of Christ.  Non-Catholics often claim it is a figure of speech but they are wrong.  St. Augustine's condemnation of taking figurative expressions literally refers genuine figures of speech, not the false claims of non-Catholics.