Comparing Flat Earth Models to Reality

I finally found a video which helped me understand the flat-earther model of a sun circling a flat earth. Thanks to p-brain for helping me out here.

Setting aside his disastrous misunderstanding of perspective, he has a decent point regarding how distant points converge at long distances.  The "plane" that the sun would orbit within would indeed appear to approach (though never quite cross) the horizon.

I suspect this claim falls apart when we start examining distances necessary to accomplish this.  Clearly the Sun isn't flying along at 30,000 ft like the contrails p-brain uses as an example.  Rather, it would need to be flying a minimum of 2-3x higher. My intuition is that the angles will come closest to working if we set the sun at an altitude equal to the radius of the earth (4000 miles) .  

So let's compare the two approaches. For the sake of simplicity, I'll assume the curvature of the sun's path is so slight that we don't notice it curving northwards. That's right, I'm going to give the Flat  Earthers a pass on the fact that we don't see the sun curving to the north! No "Where's the curve?!" from me.  

So anyways, the distinction is really easy to make. If you believe in a Flat Earth, simply measure the angle to the sun throughout the day and compare the following plot of arctan(1/x): 

If it's straight, the angular rotation is constant, which matches the spherical earth model:

1. If the solar angle matches the plot of $ arctan(1/t) $, then it's a flat earth. 
2. If the solar angle is a straight line, it's a sphere.

Note: The angle you need to measure is called the "Right Ascension" (RA).  Align a pole to point to the North Star at night. Measure the angle to the sun about this pole.  This could be done with a protractor oriented perpendicular to the pole on the back side (away from the sun). Note the angle where the shadow is cast.  Here's my attempt to draw the experimental setup.