[civilian]

But the sun isn't a single point, it is big! In the same way that a pencil can have a sharp shadow but an office building will have a blurry shadow, the satellites would produce blurry shadows.

I'm not sure of the dimensions of the inner Lagrange point-- I agree that the shadow would be centered on astronomical noon, but I think it would be so blurry, and have such a wide blur radius, as to be unnoticeable except as a change in absolute light.