I think I spot some small pieces of rough morganite. It's been a very long time since I read anything about rocks, but isn't there some kind of paper hardness color or dust test to get a rough idea of what something may be? Unfortunately the only mirror like rock I can think of is obsidian.
Fantastic rock, though. Really easy to chip away into a sharp edge to be used as a makeshift knife. Gorgeous when carved.
Can't wait. I used to be into this kind of stuff when I was younger. Huge stretch but you could try getting in touch with Yiannis Melas. He's somewhat known as a person who can pinpoint what something is in its rough form.