It took four days, but a package "delivered" by the USPS system has finally been located. According to the tracking status, the package was "delivered in or at the mailbox at 2:00 pm on April 4, 2016." Unfortunately it wasn't our mailbox.
I called the local post office and initiated an investigation. The package showed up on Friday. I was told by a manager at the post office that the package had been "delivered to a similar address." I guess that's what we refer to as "close enough for government work."