You've addressed that it can and is eliminated at 90, and we're in agreement that on this.
We need a second measurement and I believe we're also in agreement on this.
You want to use two either two observers at the same time, or less desirably one observer at different times and locations. As is said, no dice; prove the earth either curved or flat; are those proofs beyond a reasonable doubt, do they express themselves numerically?
Do you see the problem here?
edit:
Keep in mind there's a concave mirror above the refractive planes.
edit2:
Do you see the angle I'm trying to calculate? It's zero; bring the Sun down so it touches the ground then remove the refraction.
It seems that nine paragraphs isn't enough for you. Did you forget that YOU are the FE joker? All I'm doing is trying to make it easy for you to do simple math calc on your prospective FE.
Refraction is irrelevant. The straw in the glass of water - it's like being in the water with the straw.
If the earth were flat, everything I said would stand... because you could make the measurements several thousand miles apart. With FE there would be no curvature changing the 0 degrees relationship between the two people in the measurement to something that would be necessary on a globe just to make them able to focus at the edges of the sun. So, you are trying to sneakily combine GE and FE thinking.
Concave mirror is just a distraction. The center of the mirror is directly overhead, while the edges are at the 32 nm that the guys are apart, 16 nm from the the point the center is directly over.
Nothing you say has anything to do with measuring either the size of the sun, or its distance away. All your talk is a smokescreen, designed to hide the fact that you don't really know what you are talking about.
I think you are simply playing a game. But if you are sincere, then you have a religion/cult going for yourself. If it is neither of these, you are going to have to introduce a new form of math, trig, calculus, physics, and a bunch of other things. If you have these, bring on your expert physicists/mathematicians, and let them explain in detail the theories about how everything works.
As it is, you admit yourself that you are trying to do the math to prove your stuff. So you certainly aren't the joker who has a handle on your new physics.