Current progress (sorry for the interlacing).

As you can see, I can now generate the vertices of a cube of ANY subdivision amount. It still needs optimization, but it works, and that makes me happy. And I worked it out 100% on my own, which makes me even happier.
(Unfortunately, I had the idea to use Debug.DrawLine(); to visualize the points
after I was pretty much done. It's unfortunate because having that visualization would have sped up creating the code in the first place.)