Ok. So I consulted my DH after he came home tonight. His father worked as a regional postal manager for about 50 years, and DH's brother is a letter carrier to this day. DH says you might consider contacting the postmaster for your city (not to be confused with the station manager for your local post office, or God forbid, one of the window clerks (who cannot help you with this) and explaining the problem you're having. What they need to do is put in a mail forwarding/change of address for the guy since he didn't do it. YOU cannot do it yourself; it has to be done at the Postmaster level because the guy didn't request it himself. The fact that you have a forwarding (or rather, more accurately, his home address) or just any other address for them will help with this.
If this still doesn't work, then you might consider escalating the issue to the regional post office - usually the largest city in your area. They REALLY should be able to help you. But note, it's best to start with your local Postmaster, and if they don't fix it, then escalate. Meanwhile, bundle the mail together with a large rubberband and write or stamp or put a sticker on just the top one
saying "Return to Sender/Addressee Unknown/Not at this Address" and deliver at your local window letting them know to stop putting this in your mailbox.
IF that still doesn't work, then there is one last thing to do, and it will be a pain in the tuckus for you as much as for them: take each piece of mail and go to the window clerk and tell them to stop putting mail in your box that belongs to someone else. Every. Single. Time. After about three or four times, they will get tired of this and fix it for you. It's the old "squeaky wheel gets the oil" kind of thing.
Oh, also, it's perfectly fine to throw out junk mail. Bills and private looking correspondence, not so much. But there is nothing that says that a recipient must receive junk mail.
But either way, the above suggestions will likely solve your problem without you having to resort to anything you don't feel comfortable with.
Hope this helps. Good luck!