Hey Steve,
The best way to get this addressed is to contact your Account Manager and let them know so they can escalate the issue appropriately.
You are correct that since the target environment versions have different hostnames, Web Companion will not be able to switch between them. Currently, it can only switch between environments that share a hostname. You should be able to switch between QA and Dev easily, since in your example they share a hostname, but you will have to go directly to the sites that point to server-dev.example.com/tags/profile/qa/ or server-dev.example.com/tags/profile/dev/ to do this.
Thanks,
Seth