One reading (with a sextant) is taken at the horizon (0 degrees) when refraction is at a maximum and, one reading is taken at 90 degrees when refraction is at a minimum (zero refraction).
All you give me to work with is fantasy art made in Photoshop, and an arbitrarily decided apparent size for an imaginary object in an imaginary unbounded space.
Actually, the trig proofs for size and orbital mechanics of the Sun and Moon are irrefutable. That's the nature of a large number of mathematical proofs.
So the discussion really is either about how does NotBat expand his knowledge of trig to where he must accept this, or what parts of science he ignores to retain this position.