I was thinking the same thing. I spent my childhood (and, now, significant portion of my adult life) watching Picard twirl this thing; I think I'll have a pretty good intuitive sense of when it feels right.
I use a square prism as my starting shape as well. I completely agree that the original was surely made by taking such a shape and hitting it with a sander at various angles. However, this is just one of the many ways in which prop replication is much more arduous and challenging pursuit than the fabrication of original props. (Though I know that shops like HMS were often tasked with the same challenge of precisely replicating props they didn't themselves produce) We don't just need to take a shape and sand away some bits until we get a vaguely crystalline shape. We want to get as close as possible to one very particular shape, which of course is much harder.
This is why I like to try to model stuff digitally first; unlike you, Nick, I'm both bad at real-world physical art and impetuous (when I screw up a few pieces of material, I start to get frustrated). Being able to make and re-make it on my computer screen makes getting it wrong the first time somehow less discouraging. This is admittedly a failing of mine, and one of my many shortcomings as a physical maker—until recently, practically everything I had ever made had been some form of purely digital or written product—but I try to work with it.
I look forward to the application of your talents to this problem. Hopefully between the two of us, we'll figure out a satisfying solution.