The empirical evidence for EA seems to be the observations it is used to explain.
The idea that anyone should be "explaining observations" rather than drawing conclusions from them is at the core of the disagreement here. We're not trying to "explain sunsets", despite the repeated cries of those who claim to support science, but whose actions betray them. We observe, hypothesise, verify, and conclude.
EA is partially hypothesised, and at no point did verification suggest that there's any reason to stop developing the theory.
Maybe "understanding" is a better word that "explaining"? That's what science has sought to do - to understand.
The sun clearly goes across the sky and sets - the ancients believed that it was the sun that moved, their flat earth model had the sun above the earth during day and below it during night. Day was day everywhere, night was night everywhere. We now know that isn't true. So we need a different explanation or understanding of how the sun moves and why it sets.
Your page on Zeteticism says:
in questioning the shape of the Earth the zetetic does not make a hypothesis suggesting that the Earth is round or flat and then proceed to testing that hypothesis; he skips that step and devises an experiment that will determine the shape of the Earth, and bases his conclusion on the result of that experiment
But how does one do that? What's the experiment? We know the sun sets. Let's say that a rotating globe earth and your FE model with EA yield identical results. Why would you conclude one of those rather than the other?
You have said that you believe you can "see too low", so I guess that's a test you've done - making observations of distant objects. But I think you accept that you can't see
all of distant objects. So now what? Conventional science would say that you can't see the bottom of distant objects because the earth is a sphere and the bottom is hidden behind the curve of the earth. And if you can see more than your trusty curve calculator tells you that you should, then it's because refraction is a thing - a thing one can easily demonstrate. But now we're back to the same problem. If FE+EA would also yield the same results then why is one conclusion preferable to the other?
What's the test that makes you favour FE+EA over a globe earth?