You can use your SSH to create a SOCKS proxy VPS connection to WordPress. Its very simple to set up a dynamic port forwarding in a SSH client vSSH.
This procedure gives you a VPN connection. The SOCKS VPN setup enables you to access the Google PageSpeed admin page and WordPress through a secure tunnel. All you need is an SSH client on your PC. Nothing to install or configure on the server side.
Unfortunately, this does not work on iPad and iPhone.