After my third request for a refund, Living Social sent me a stock email back:
Your refund request is outside of our policy. If you would like to accept the courtesy Deal Bucks, reply to this email to let us know, and we'll be happy to credit your account with Deal Bucks equal to the paid value of your voucher.
If you still have questions, please reply to this email. We're happy to help.
I politely informed them that I would be disputing the charge with my credit card company, and they told me to politely fuck off (okay, they said they were "sorry [they] weren't able to fulfill [my] request today.).
I called Visa and had the charge credited to my account in under ten minutes. Thanks, Visa! The only caveat is if Living Social can prove I received my items, then the credit will be removed.
Now it's just a waiting game to see if Digital 007 will refund the shipping I paid for, but it was only a few dollars, so I'm not overly worried about it.