Dear dysfunction,
Let me provide an explanation about that ship that bothers you so much. I am not sure if it is true, but it seems to be reasonable and may work. I shall try to operate with very obvious things that could be easily verified.
First of all, I have never personally observed that illusion of a ship sinking below the horizon. If what you say is true, the explanation might be the following.
What I observed many times while driving was that a distant part of the road became much like a mirror and, when the weather was fine, often even seemed to disappear, merging with the sky. You probably are also aware of such a phenomenon, too. Why is that? The road is apparently not a mirror. You can always stop the car and check if I am telling you the truth. First of all, the road is most often grey or dark. Then, it's surface is neither polished not even, for it contains many irregularities: particles, small stones, paint etc., and most of them are quite noticeable even from some distance. Nevertheless, a distant part of the road looks like mirror, reflecting light and apparently covering the irregularities.
My explanation is that when I was looking at a distant part of the road at a very small angle, I saw the reflection of the light from a thin layer of air covering the surface of the road and its irregularities. That is why the distant part of the road appeared like a mirror, and I do not see any other explanation. That layer of air over the road must obviously have had a certain depth, which was enough to hide from me both the imperfectness of the road's surface and small objects laying on it.
It seems quite likely that a similar phenomenon over the sea surface might lead to your illusion. The ship is not sinking below the horizon. Instead of that, you are observing it at progressively smaller angles and, when the size of the hull becomes visually small enough, that air layer over the sea surface hides the hull from you, so it seemingly disappears. The masts are higher than the hull, and that is exactly the reason why you still see them for a while. Since the sea surface is highly reflective by itself (comparing to the road surface), the difference between the distant part of the sea and the rest of it is not that obvious as in the case of the road.
I do hope I satisfied your healthy curiosity. Again, I am not sure if this is a correct explanation but it seems to be a good working hypothesis. There are many optical illusions in the atmosphere, but it seems to be no need to invent such an extraordinary reason as round Earth to explain them. People often saw two (or more) Suns, green beams etc. etc., so what?
Also, may I humbly ask you why, when you see a ship sinking below the horizon, you believe that this is what's really happening? After all, isn't it the very RE theory itself that constantly teaches us not to believe our very own eyes? We clearly see that the Earth is flat; no - they say us! it is round, but we do not see the "roundness". Everyone in healthy mind sees that the Sun is going around the Earth; no, they say, the Sun is OK, this is the very Earth that is going around the Sun and - on top of all that - is also rotating around its "axis"! What an unbelievable lie! If the Earth was rotating, making the full turn every 24 hours, as the RE theory tells, its equatorial part would be moving with supersonic speed. There is absolutely no proof of that, no shock waves etc. On the basis of this alone, the false theory of RE ought to be dethroned and replaced by another, true, theory, that restores the human dignity and asserts, once and forever, our irrevocable right to believe our own eyes and our indispensable freedom to make our own conclusions.
Dixi