That is what keeps me from believing flat earth, that I have not come across a coherent system describing and modeling it. I might have missed it in this thread though.
So, there are two logically distinct phases here, and they're always conflated by the globe advocates, on purpose.
First, there's a mountain of evidence that falsifies or invalides the globe model. Period.
So, according to the scientific method, you have to them provide a new hypothesis that explains this additional evidence.
You could in fact try to posit a globe that's, say, 10 times bigger than what they tell us, and this would explain some of the aberrant data, observations, and evidence. Then you would test it to see if explains everything.
There's this begging of the question that the globers engage in, where they simply assume they have a valid model. That's the entire point of all the FE evidence, that "no you don't ... your model does NOT work".
Then you add to it that nearly all ancient cultures had a flat earth cosmology, and to Catholics that means something, even if it doesn't for the evolutionists. So, the latter hold that these were just a bunch of idiots and eventually learned better, as they progressed from out of the primordial soup, to grunts and groans, to using some primitive tools, and eventually stopped worshipping as a god everything they did not understand. But Catholics have this notion of what's called "primitive revelation", where Adam (and Eve) had a complete and perfect knowledge of the natural order, and so if disparate cultures around the world had the same cosmology, there's a good chance it derives from Adam's knowledge. It's very similar to the "universal consensus of the Fathers" criterion for Revelation and doctrine, where if all the Fathers scattered around the world say the same thing about some doctrinal matter, it comes from the Apostles and is part of the Deposit of Revelation.
Speaking of the Fathers, Sacred Scripture is entirely clear in describing a solid firmament above the earth, given its properties, where it keeps waters above from inundating the earth ... and there's no modern cosmological model that even comes close to accounting for it. Modernist "Catholics" claim that the "firmament" is just a poetic way of describing "space", but that's nonsense if you actually look at what the Bible says about it and what the Church Fathers unanimously said about it. Dr. Sungenis tried to explain it with a "Planck Fabric", and then later an Ice Ball / Dome ... but even he has to admit that just empty space absolutely does not cut it. I think he abandoned Planck Fabric when he realized that it couldn't account for being something that kept watrs from inundating the earth.