I've had some luck doing LinkedIn InMail to various high-level people at large companies to get support.

Once I used Inmail to get a DHL SVP to get his executive assistant to follow up why my package hadn't arrived... The assistant Cc'd me on messages a Friday afternoon and made it clear said SVP wanted updates. Monday morning the package that I had been told was on a ship being returned to the seller in the US arrived from a depot 5 minutes away from my office in London.

I'm guessing most people at that level are so insulated from their customers experiences that getting a request like that is totally novel for most of them - it's worked for me several times.