I've read the FAQ to see how you explain seasons, and you say the radius of the Sun's orbit changes throughout the year. So I assume then at the equinoxes is orbits directly above the equator. Then at the equinox every point on the Earth receives an equal 12 hours of sunlight on the equinox. So let's consider a point on the equator. Clearly on this day then, using your model, one would assume the Sun would be visible for the 12 hours it is closest to this point, and not visible when it is 12 hours away from this point. Since your model's diameter is 29,000 miles, the diameter of the circle formed by the equator would be 14,500 miles, so the radius is 7,250 miles. Then doing a simple calculation, the point where the sun "sets" at our hypothetical point on the equator would be:
sqrt(2 * 7250^2) = 10,253 miles away on the ground
Then since you assume the Earth is flat, the Sun would always have to set when it is directly above a point that is 10,253 miles away on the ground. Clearly then, any point that is less than (10,253 - 7250 = 3003) miles away from the north pole should receive 24 hours of sunlight on the equinox, since the sun would never be directly above a point more than 12,253 miles away from the point we are considering.