I know this podcast was a long time ago, but I'm relatively new to Claytemple media, so working through the back catalogue on an "as can" basis. Thoughts:
Some of the themes you discussed reminded me very much of Sweeney Todd. However, when I checked the dates, that story came out several years after this one. I was not able to find out if this story was an influence on Sweeney Todd, but I would not be surprised if it were.
I liked that you called out that the rule of physics are different in this world. I had never thought of it before, but yeah. If the head was severed from the body, how did it land so as to look attached. Not to put too fine a point on it, a razor is a fairly fragile blade and no one that could sever a head from a body using a razor without a lot of careful work.
This story was published in 1841, when both the memory of the French revolutions loomed large and the Hungry 40s were just starting. It's an interesting time to make a fallen aristocrat a focus of the story.
My take on the presentation of the orangutan was very different than yours. Apes have been used as racist symbols for a long time. (King Kong, anyone?) I read the story's take as "Damn shame they took it out of the jungle, shouldn't have happened, but now that it's here we have to keep it in a cage. "
Because Poe down played parts of his background, people forget that he spent a considerable part of his childhood in Virginia. He grew up around slaves and the aristocratic mindset that was prevalent in the antebellum South. I see a lot of these attitudes in this story.
My degree is in computer science, and we distinguish between conceptual complexity and combinatoric (or combinatorial) complexity. Poe seems to be trying to make that distinction. However, he sort of anticipated the way modern AI works. To oversimplify massively, collect a massive database and have an algorithm look for patterns.
FWIW: This read as a parody of reason to me. I didn't get a moment of Poe taking Dupin seriously.