
I remembered that when building the prototype box out of LEGOs, I had determined that they are not actually square. 1x1 LEGO bricks are slightly taller than wide. I snapped some together and made ruler and protractor measurements. Some diagrams and geometry later (I hope you are proud, Mr. Burkhardt!), I can see that the 10 degree deflection might be a factor here.
Close to the glass, the light rays have a much smaller delta-x. At the far end, they have a more considerable delta-x. That might not seem important, except that the camera hole in the box is much smaller in diameter than a dime. Also, a clip-on macro lens for an iPad isn't the same as a true camera macro lens. In the camera, the lens is much further from the CCD, so peripheral light that strikes the border of the lens can still reflect down the tube and reach the sensor. Here, with the lens almost right up against the camera, only the center of the lens really matters.
I am wondering if I can elevate the bottom edge of the glass ever so slightly to get closer to 45 degrees, and see if that makes a significant difference. I bet it will, since it's obvious that the coin area closest to the glass has much better illumination.