That isnt how it works. The speed of light is the speed of causality; it doesn’t have anything to do with light. Its just the fastest speed at which things can happen. Light, being massless, happens to travel at that speed.
In your scenario, the light beam would just be stretched along its length and the 2D interface on the surface of the moon would just “lag behind” from your POV. But it would lag at the speed of light.
I’m agreeing with your conclusion but not with your reasoning.
You reason that since it looks like he might be innocent, he shouldn’t have been executed. Extrapolating from this yields that you also believe that if you felt he was definitely guilty, he should have been executed.
I’m saying that because this uncertainty exists at all as a concept the death penalty should be abolished. Its impossible to prove someone’s guilt 100% in these cases, therefore the death penalty is immoral. Not just in this case but in every case.