That's got me thinking... I wonder if you could use that as the name (current resident) in the USPS forwarding services found online? You would only need a throwaway email address to create an account and set it up. This might merit a test.
For me, I'd route it to my old address.
I dislike the current resident there anyway.
I don't understand the part where you mention the carrier directly placing mail without it being processed.
Why does that happen? How does that work? The carrier gives that to all mailboxes?
[0] https://www.usps.com/business/every-door-direct-mail.htm