LinkedIn InMail has worked for me in the past with e.g. DHL.

A package they claimed was on a slow boat back to the US to be returned to the sender mysteriously turned up in a depot 5 minutes away when a Senior VP's assistant asked for updates on behalf of said SVP and Cc'd in the SVP and me.

Emails went out Friday evening. Package was in my office Monday morning.

A lot of these channels work as long as few people use them. You surprise people who are not used to be confronted by their users unreasonably painful experiences.