I have noticed that (Trad) Catholic Globers have VERY LITTLE when they try to argue that the Church pushes globe earth.
They have the Globus Cruciger, and the "rotundus" of St. Thomas Aquinas, and little else.
Scripture, meanwhile, is VERY heavy-handed as it comes in strong on the side of the Flat Earth paradigm. Also, the Hebrew conception of the universe is literally a flat earth under a dome Firmament.
Not to mention all the pagan nations of the earth, dispersed from the Tower of Babel, have the same conception of the universe, more or less corrupted (just as they have the notion of a Redeemer, a Garden of Eden & Fall of mankind, and a global Flood of Noah).
Adam and Eve knew from God that the earth was flat. They passed this on to their children. This transmission of knowledge down the generations from Adam's knowledge is called the Primitive Revelation.
They really have to "reach". They're scraping the bottom of the barrel for evidence. But here's the funny part: there is ZERO mention of the rest of the "package": an infinite universe, moons orbiting planets, gravity, pressurized air held around the earth without a container, other terra firma worlds that could theoretically be landed on, 4+ different kinds of movement of the earth, various wobbles and rotations of the earth, sun, galaxy, etc.
In other words, there is certainly NO mention anywhere of the whole NASA package. And yet that is what some Catholics try to read in to these meager sentences, such as "rotundus" of St. Thomas. Talk about desperate, and confirmation bias!
St. Thomas also said that the pelican tore its own flesh, so it could feed its own gore to its offspring. This was a commonly held belief at the time -- which we now know to be factually false. So keep that in mind as well.
Your last point renders the huge amount of "ink" spilled on St. Thomas' opinion on the matter entirely moot. I don't think it's at all evident what his final opinion was, but EVEN IF HE DID THINK THE EARTH WAS A NASA BALL ... so what? He wasn't a scientist but a theologian.
Of course, the other problem these guys have is that when they the word "sphere" (or sometimes even "round" or "circle"), they immediately assume the NASA ball model, but even the FE model has the earth being a sphere, just that its sphericity includes the firmament as part of the earth ... and this is where they say this with the space pancake in the backs of their minds.
At the end of the day, they have absolutely NOTHING, just "muh NASA" and constant begged questions. So, when they distract by saying crap like "where's your map", they beg the question that globe has a working map. I asked this latest brainwashed troll which was HIS map of the dozen or so projections, all of which contradict one another. Herve Riboni actually went out into the field and demonstrated that Google "map" does not actually reflect reality, and he explains how they use "magnetic declination" to hide the globe and to explain away why it is that you cannot navigate (primarily the Southern "Hemisphere") with merely a map and a compass ... which you absolutely should be able to do if they had an accurate map.
Most of all, however, none of them can explain why and how we can consistently "see too far", even when in some cases the objects should be hidden behind literally miles of curvature.
Nor do any of their cosmologies explain the firmament
At the end of the day, they longer I've been involved in this debate, the more I realize that they've got absolutely nothing besides their assumption that modern science and NASA are telling the truth.
When they imply that FE is falsified simply because we don't (yet) have a 100% accurate map (due to lack of necessary resources), they layer fallacy upon fallacy. Not having an explanation for everything does not suffices to falsify a hypothesis. They must adduce evidence that actively contradicts the FE model in order to actually falsify that. In addition, as I mentioned, the point also subtly (and dishonestly) begs the question and pushes it as known uncontestable fact that the Globers DO have answers for everything ... despite the fact that Kaku said that there's never been a greater mismatch between theory and observation in the history of science than in the current state of cosmology. Simply Google "scientists are baffled", and you'll see many millions of hits. What the Globers have are many THEORIES about this, that, or another aspect of the natural world, but the churn regarding these theories is almost legendary, where every other year someone questions the previous "orthodoxy" as having been wrong. But the "scientists" have long engaged in this tactic of presenting their theories as if they were known fact. Take for instance, the nonsense about what's beneath the surface of the earth, the layers, the core, the mantle, etc. ... all those diagrams they brainwash you with as kids ... these are presented as proven, uncontestable fact, whereas the reality is that it's nothing but theory, since NOBODY actually knows what's down there and the deepest little hold that's every been dug is merely a tiny fraction of the way down in to the earth ... and what's funny is that when the Russians dug their hole, they were CONSTANTLY surprised by stuff they found that, per their theories, shouldn't have been there. So if they had 100 things per mile that was not accounted for in their theories ... then their theories are hardly worth the paper they're written on, but this does not prevent them from presenting them as fact, just as they have done with evolution, the age of the earth, the geological strata, etc. etc. etc. --- pretty much everything anti-Christian they present as proven fact, and they do that toe undermine and destroy faith ... but unfortunately we have a bunch of weak-minded brainwashed Trads who should no better just sucking it all in anyway.