The SSH tunnel option has the SSH host itself, and your connection to the tunnel (localhost:{port}) but no where does it ask for the remote host that the connection should be forwarded to.
Could you try to specify eshost.private.whatever.com:443 in URL field on the General tab and ubuntu@remotehost.whatever.com in Host field on the SSH tab?
The SSH tunnel option has the SSH host itself, and your connection to the tunnel (localhost:{port}) but no where does it ask for the remote host that the connection should be forwarded to.
For example with a SSH tunnel:
I would connect to localhost:10443 as my connection, but notice I need two other hosts specified. The plugin does not have this option.