Load up HLL. Add all servers to favorites by clicking the tiny star icon thats next to the servername. Alt-tab back to Steam. Right click the Steam icon in the taskbar. Choose “Servers” – Choose “Favorites” tab. All the servers you added in HLL will be right there.
This has solved one of my worst nightmares of HLL. Huge relief. Hopefully it works for many more!
* For anyone who needs to activate the server tab within Steam: Settings>Interface>Set Taskbar Preferences on the bottom.