Flat Earth query

I seem to be seeing a lot of stuff about flat Earth recently. Whether it really is on the rise as much as I seem to have seen or whether I'm just noticing it more is another matter. Either way, I've seen a lot of flat Earth posts recently.

Now, I happen to believe in the scientific method, in that any theory should allow you to make predictions on what will happen in a certain set of circumstances. You can then do a test and compare the result with the prediction. If they match, the theory is good. If they are miles apart the theory is bad and you need to find a new theory. If they are close then there may be some mileage in modifying the theory and re-trying the test.

So, that said I am quite prepared to be convinced that the Earth is flat if someone can show me an accurate prediction that model makes which the equivalent round Earth model does not.

Here is the first prediction that I can make with the flat Earth theory: Something passing overhead will appear largest when it is directly above me and as such at its closest to me. As it flies away from me it will appear to get gradually smaller and smaller until it eventually vanishes from sight - not because of the curvature of the Earth, but just because it is so far away I can't see it any more.

Here is the first observation I can make which contradicts that prediction: When the moon comes up, it appears on the horizon and is already large. In fact, if anything it looks larger when on the horizon because you have a frame of reference to compare it to in the form of trees or buildings or whatever you have in sight. When the moon is at its highest and as such at its closest to me it is not at the largest I will see it. As it moves past it gets no smaller and eventually it will go back down to the horizon where, if anything, it will look larger again.

So, I've made a prediction based on the theory and the observable facts are completely different to the prediction, implying the theory is bad.

However, on the flip side, if the Earth is round and the moon orbits the Earth then the prediction will change: Since the moon stays (more or less) equidistant from the planet and is very far away from the Earth, its distance from the observer will only change by a very minor amount while it moves overhead, meaning it will appear to be the same size at all times.

Suddenly the observation and the prediction match, implying the theory is good.

So how is that explained within the flat Earth model?