Anyhow, I don't think it's the GetMine() method I need, it's the GetPersonalEntry() method. Took me a while, but I finally figured out how to use it.
Incidentally, is there a boolean I can call if the Leaderboard fails to load? I.e. if the player is offline. I just want to use it to display a message if the leaderboard fails to load (I see that the servers for it go down frequently as well).