It is not automatically true that everything would need to be different. Light can still, and should still, behave as it does on a round earth.
Everything would not need to be different, but observably many things would be. If light behaves identically on a FE and RE, how do you explain sunset and the horizon?
There clearly is a need for light to change its properties, or at the very least for something else to influence. You're working under the assumption that the RE model is the only necessary one, and should be treated as a default: that is a useless perspective when I'm trying to determine a FE model.
1. The extra energy come from? or:
2. The excess energy go?
There are many sources for energy. The excess energy may have gone into the light and heat produced by the Sun, or into the mechanism that keeps it moving: and could come from similar places. There are virtual particles, for another source of energy: and if you accept a UA model a near-infinite source of energy is involved.
Regardless, in reality there are knock-on effects. Something used to explain one thing may end up having an effect in a completely different setting: perhaps an atmospheric anomaly that causes the Coriolis force would also interfere with readings of things that pass through it. Sheer speculation, merely an illustration. Uncomfortable conveniences feel less like an assumption when the same principle applies over dozens of areas.
Probes going close to the sun has nothing with light to do. You don't need light to behave in a certain way to use rockets, as they don't depend on light. And my point was that any change in light behaviour would be noticeable when you are much closer to the source. If no change then either there is no unknown force or it is way to weak to mess with our perception of the sun from earth. And you have admitted in another thread that you believe space travel is genuine.
I have said I favor that idea, I have not fully accepted it yet, until I can run the test.
Rockets don't depend on light, but their observations clearly do. Changes in the behavior of light are only noticable if you expect to see them: light is the one thing it's very difficulty to observe, because you rely on it in order to perform any observations.
And for the discussion, the important part is that light does not change it's wavelength as it travels. As this would require energy or create excess energy it won't work in an empty vacuum of space, where there is nothing to draw the energy from or give energy.
There is plenty of energy: vacuum is the lack of matter, not of energy. Cosmic radiation, sun and starlight, in just the RE model. In the FE possibilities we could have a dome or an accelerator.