> I don't have the tools or knowledge required to sand this down to a perfect mirror finish
I did a resin cast that had a similar "lip" at the edge (I turned a LGA CPU socket into a coaster), and I was able to sand it down fairly easily using regular sandpaper of progressively higher grit, producing a more or less perfect cuboid. The flatness was achieved by taping the sandpaper to a flat surface, and moving the part.
It's been a while, I can't remember if I used some kind of polishing compound at the end or whether the sandpaper alone was enough for a good finish.
I suspect you're right, but knowing myself I'd quickly get sick of sanding (6 faces with 5-6 different kinds of sandpaper), and I'd want an orbital sander. Then I'm pretty sure you want to polish the surfaces: lots of elbow grease or a polishing/buffing tool. If I had a workshop with space for tools and dust I'd probably go for it, but I'm doing this in the living room of a small apartment.
This would be a similar process to finishing any painted surface. Progressive through the grits, each time removing the scratches from the previous grit, wet sanding with the higher grits. You can then hand polish with polishing compounds you can get at any hardware/car accessory store. You can start with an orbital sander or a belt sander of some sorts. I've done this on guitars I've built.
If you're fairly close it shouldn't be a ton of work.
Could probably cut this into a cylinder on a wood-lathe; you can do some pretty good polishing on one too ala polished wood pens. With skill you might even be able to round the end.
I did a resin cast that had a similar "lip" at the edge (I turned a LGA CPU socket into a coaster), and I was able to sand it down fairly easily using regular sandpaper of progressively higher grit, producing a more or less perfect cuboid. The flatness was achieved by taping the sandpaper to a flat surface, and moving the part.
It's been a while, I can't remember if I used some kind of polishing compound at the end or whether the sandpaper alone was enough for a good finish.