Well, I don't believe him. It is Claude all the way through. There are more markers than just those. I covered some in my more comprehensive review of it, but tbf that one is a bit of a mess.
I don't see how my point about the erroneous date makes your point. He POSTED IT with that date, and only changed it AFTER someone pointed it out, then BLOCKED them.
If he did write it by hand though, that means he is admitting to plagiarising the sources, and also to framing that makes absolutely no sense, like saying Schwartz didn't say something that he literally did say. So, great job I guess!
I fully believe that he used only a general prompt, and anything in the essay that seems specific, Claude has mined from the sources. I am going to try to reverse engineer the prompt.