A personal perspective.....
We are taught that the ancients were somewhat primitive in thought process (contradicting the philosophy of the time clearly and evident to be conditioned in education that only noble and educated men can and, could ever think for themselves) Wise men pondered on global Earth while a stupid and primitive layman had belief in an Earth in which we could fall off the sides.
I get so annoyed at this because it is simply not true and there is no evidence other than modern scholars stating this was a fear for the silly uneducated fools - There is no documented evidence that people believed they would fall off the edge - Many people mock the Flat Earth understanding on this fiction. The misleading of actual historic belief - the religious evident a dome like protection, if not religious, an understanding of walls protecting the inner `circular` Earth model - Egyptians, Hebrews, Babylonians..... All very wise and non primitive examples.
This is very relatable. It really isn't true that people dreaded the thought of falling off the earth, it's a result of ignorance-based stigmatism. Sadly that ignorance cuts both ways, with some FEers claiming that if gravity existed, it would still pull people downwards in an astronomical frame of reference and make people and objects in the Southern Hemisphere fall off, rather than pulling inward. One somewhat more reasonable cause of the condescension is that many of the concepts of nature at the time were based more on philosophy than observation.
Nothing we are taught and given to date provides accuracy it only ever is met with defiance if questioned - The point I am making, the agenda in which to be taught something and a demand you believe it seems more important in the world today by those providing the what we should be educated and this will never sit right with me. Not religiously, scientifically, politically, philosophically....
This is the case because "guaranteed facts" of science are based
very heavily in proofs and logic. RET is considered fact by science because of the proofs and logic behind it, and that's why many think it's so ridiculous to claim it's false. (Note: I'm speaking subjectively about how people feel about it, not objectively about whether that statement is true here.) Some things, because they undeniably are based on undeniable logic and proofs, can really be considered facts--this happens a lot in mathematics, for example. If one don't believe the Pythagorean Theorem to be true, people will naturally think that person is stupid.
Nothing we are taught and given to date provides accuracy. . .
Many other things, like the theory of gravity or relativity, are accepted as the most
probable explanation of something, generally on a best-fit basis. Based on observation, theories
are made more and more accurate and can sometimes predict other phenomenon. For example, Einstein actually predicted the recent discovery of gravitational waves. [nb]While it's not really a theory, the Periodic Table is another good example. Mendeleev found that by organizing the elements by mass (and therefore also proton count and neutral-charge electron count), they were grouped by their properties (because of the electron counts). Because of this, Mendeleev predicted the properties of unknown elements with remarkable accuracy, and some of those were even found because scientists searched for them
by those properties. Because they're grouped by mass, valence electrons, and properties all at once, it's the same organization we use to this day. [/nb] If someone were to say they don't believe a theory like this to be the case, they'd most likely be told to prove it wrong or prove something else is more accurate, only because that's how science works. If someone really does prove it wrong, it's accepted as wrong, a new theory is searched for and developed, and science moves on.
If someone were to say they don't believe another theory to be true, one less substantiated by conclusive observation and experiments like evolution, less people lose their minds over it, because less-proven theories are judged more on a best-fit basis than absolute proofs due to the lack of more conclusive evidence. (I don't mean to turn this into a creation/evolution thread, there
is notable division over whether evolution properly explains things, so I'm using it as an example.)
In short, science really is all about accuracy, and people are only ridiculed and opposed if they try to deny something without a proof that it's false or a better suggestion; the more accurate the better, and the less mutable it becomes. It gets harder and harder to come up with a better suggestion, so less and less reasonable to doubt it. If somebody strays beyond this reasonable boundary and forces a belief without proper proof, then no, it shouldn't sit well with anyone.
I cannot determine a belief other than an understanding of we very well could be the complete opposite of what we have been taught we are - Like yourself, I need not only explanations but, hard evidence
Science!
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That's the point and mentality of science, all is possible unless proven otherwise. The most probable best-fitting remaining theory is the one assumed to be the explanation until scientifically proven otherwise. New theories should cover more of the observable universe and/or have less logical holes in it.
The southern stars.... An interesting one - I like the mirror ball explanation that expresses lights contradicting movement of clockwise/anticlockwise but, know it would take more than one experiment and understanding to grab and decide upon (as should we all concerning the alleged great minds of which science lays its foundations upon today and have many arguing as to whether we could think for ourselves and contradict )
The main thing about that theory is that the stars still rotate in the same direction when viewed from the equator. The reason they move CW/CCW in the North/South according to RET is a difference in viewer orientation on a uniformly rotating Earth.
How have I misunderstood the scales involved in perspective? (again I ask respectfully because I truly do not understand)
First off, remember the horizon is (RET) where the curvature of the earth blocks our vision from seeing any farther.
The size ratio of us to Earth is much smaller than that of an ant to that crystal ball. Our eyes are about an inch or less in diameter and Earth has a diameter of thousands of miles; curvature is imperceptible through unaided observation. Especially when we're looking out over land, because the surface is very irregular, unlike that crystal ball. Also, when we're looking
around us from the surface, the horizon will be just about level because of the irregularity and the scale. If someone is in a plane or orbit, they have a more distant view of things. From a higher level, you're not looking out at the horizon so much as down at the horizon.
Essentially, when you view it from the elevation of your own height, you're up too close and the curvature is imperceptible due to the size of our eyes. The higher up you go, the more of Earth comes into view, until you definitively the horizon block out the other side of the world in a manner befitting a spherical shape. Perspective shows less overall detail when close up, and allows more when you get farther away. (Again to everyone please don't just say "That's wrong cuz it's flat," OP is asking for an explanation of how it would work on a round Earth and that's all this is.)
I am leaning more and more towards a belief of the ancient understandings of a circular Earth surrounded by walls mainly because there is so much evidence of history having been mocked and rewritten to fit an agenda of learning and memorizing other peoples understandings and deliberations of fact (again, religiously, politically, scientifically and especially historically) - There is much documentation proving ancient civilizations knew about stars and locations millenia before NASA (in fact the majority of our modern understanding stems from ancient knowledge - yet still we are told how idiotic they were). This alone cannot be ignored (for me at least) I will indeed look into the southern stars because that is very interesting 
It's good to reconsider the basics and consider all possibilities every now and then. It's important not to let subjective things--what's been stigmatized and by who--affect our view of empirically verifiable matters. The difference between what was adopted by modern science and what was mocked by history is who had more proof of what they were saying, which is the most important thing. Letting a conspiracy theory be your primary proof is another sure-fire way to break up proofs of your beliefs. They're rarely ever conclusive evidence logically speaking. [nb]For example, even if NASA faked space travel to win the Space Race and help boost Cold War morale, it could very well be that they got stuck on a slippery slope technologically and that's why we don't have space travel, rather than because Earth isn't round. Conversely, if Earth is round that doesn't mean NASA
does have space travel. Just because the Freemasons or Illuminati believe Earth is round doesn't mean it's not. Et cetera. In matters of conspiracy,
nothing can be viewed in black and white. Many conspiracies have been exposed in the past, but it requires narrowing down a lot of possibilities, often through proofs, and sometimes a bit of dumb luck. Reminds me of an episode of Doctor Who featuring Agatha Christie. Somebody confessed to faking their paraplegia to guilt his wife into staying with him because he thought he had been found out, when Christie was really just going to declare him innocent. Sometimes things just come out.[/nb]
Quick rehash:
Kudos to you for deciding to reconsider the shape of the earth.
Just make sure you decide your final beliefs for the right reasons, either hard evidence or greatest explanatory coverage.
If somebody seems to be forcing a belief on you from RET or FET or really anywhere else, always give careful consideration to the validity of the causes for their conviction before rejecting it. as
Again, sorry for not realizing sooner that my first reply failed to send.
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) they usually show visual footage because it's interesting to look at and I'm sure useful for meteorologists. Sorry I don't have any sources for you right now.