Moon Illusion explained (my attempt)

I and others have been aware of this particular illusion concerning the moon where the angle of illumination on the moon during a phase does not match what you'd expect by drawing a straight line to where the sun is in the sky. When I encountered this at Jerry Lodriguss' site here: http://www.astropix.com/HTML/L_STORY/MOONILL.HTM I thought about it, sketched a few crude pictures and came up with these seemingly obvious observations (which may or may not be true).

In the first diagram, I replaced the moon with a pole that has 3 spheres impaled upon it and a screen upon which the shadows might be cast. But in actuality, this is wrong because although the sun is to the RIGHT of the pole, because it is so distant the rays almost entirely render the spheres (and tree) backlit, and the shadows would miss the screen completely. And even if the sun were further to the right so the shadows would fall on the screen, they would not appear to be lit at different angles nor have their shadows spaced more widely on the screen in accordance with lines drawn from the sun through the spheres and onto the screen. The second diagram better illustrates what we'd see. How does this apply to the moon?

In the third diagram, the moon replaces the spheres. Although the moon IS far away and much larger than it appears, for all intents and purposes it is (I imagine) closer in scale to the model spheres ON the earth RELATIVE to the size of the sun-moon-earth system. The third diagram shows a large angle between the sun and moon - and I don't even know what this angle between the horizon and the sun/moon signifies, but it seems to play a part in the illusion. In the final diagram I consider the true distances and sizes involved (not to scale!) and, even though the numbers and scale are wrong, you can see that INCREASING the sun from the earth and moon results in a SMALLER angle of (apparent?) separation, compared to how we see th eillusion ON EARTH. I'm not sure, but I think I'm on to something...