How To Occasionally Pin The Hotkey Window To A Specific Desktop

I am running iTerm2 build 3.3.6. I usually just bring up the Hotkey window with a keystroke, but occasionally I want to keep it open on a specific OSX desktop and only that desktop. That way I can hop to another desktop to look at reference material and back. Right now, the iTerm Hotkey window follows me from desktop to desktop when pinned open. Is there a way to get it to stick to only a specific desktop? Ideally, hitting the Hotkey shortcut would bring it up on whatever desktop I happen to be on, so I could have it stuck on a specific desktop until I want to look at it on another desktop, but that is a different matter. I am using TotalSpaces for desktop management, if that makes any difference.