@porkpal - I didn't see the actual seed anymore than is visible in the first few photos. Since I wanted to keep the tree alive, at least until I figured out what it was, I was afraid to dig too deep and damage the taproot.
@Daisyl @Henhouse - I completely forgot about the scratch test. So... rubbing the leaves doesn't smell like anything. Scratching the stem with a fingernail (not rubbing, that has has no smell, I have to actually abrade the surface) has a smell, but I don't know if it's a walnut smell. It's just sort of a... green, fresh, slightly sharp plant smell?
I'm sorry, I have a strange olfactory system, and certain odors allude me (when I was in High School I loved the smell of pumpkin so I bought pumpkin bar soap once for the shower... couldn't smell it at all. Bummer. Figured the brand was a bad brand, but then a friend was over shortly after I showered and they were like wow, your house smells like pumpkin! I've since encountered this in other things. So I think there's a chemical 'pumpkin replacement' I can't detect, etc.) So it's possible that I'm not the most qualified to sniff the tree. ...Probably won't ever use that last sentence again.
Any other tricks y'all got up your sleeves?