I think it was on... 10/14 or 10/15 I finally finished the "A Miner's Life for Me: Eorzea" achievement. When I finished it, I didn't receive the pick. I noticed after the fact that my main hand armory chest was full up, so I assume that is where it was supposed to appear. A quick google and forum search and I was unable to find out where I was supposed to receive the axe. I tried removing some main hand weapons to free up my armory; I tried messing around with the achievement page, looking for a "receive rewards button" or something; I tried checking the mailbox and the Miner's guild all to no avail. Finally I tried waiting a few days before posting here.

I'm posting in hopes of either a dev responding to this or someone who knows more about this responding and saying "oh you idiot, all you had to do was X to get your pick!"
Anyhow, thanks all