Have you considered using a registered agent service, e.g., Virtual Post Mail and Earth Class Mail? They do this, along with other services like check deposit, and it's only marginally more expensive than a PO box.
Edit:
They're also who I thought this was about. I get Startup.com and Start-up Junkies mixed up. Start-up Junkies followed Earth Class Mail, and was also pretty interesting.
Yes and no. I really want the service as part of my local post office.
I wish I could keep my current PO Box that I've had for years but still have some of these features.
It would be awesome if the Post Office could:
A) Let me know mail has arrived, and from whom.
B) Mail be a box full of my mail once a month to my physical address. That way I can either drive in and get it, if it's urgent, or just wait for the box.
http://www.geekwire.com/2015/heavily-funded-earth-class-mail...
Edit: They're also who I thought this was about. I get Startup.com and Start-up Junkies mixed up. Start-up Junkies followed Earth Class Mail, and was also pretty interesting.