Just excellent. I'm mightily impressed by your characterization of Cuthbert -- his patterns, his symmetry, his matter-of-fact style, his literalism. You've created a powerful portrait of someone on the autism spectrum; you've made such sense of his world. As I read, I felt so clearly aligned with him: his pov became mine, and it was the "normal" world that seemed odd.
I also love the way you've incorporated the other denizens of the HP world, particularly Albus and Filius; I love that Cuthbert's father understands a bit of how the world looks to him; I love your explanation for why he chose to remain a ghost; I absolutely adore all the historical apparatus and the precise details. And Walburga -- as others have said, you have not excused her, but you've made her plausible and made both her and Cuthbert's heartbreak real.
What a great conception of Binns. The whole fic is a triumph.