I got the toggle working, but couldn't get background transparency.
Proper quake mode is just one shortcut to show/hide the entire terminal window, otherwise the app is completely hidden from the app switcher and the dock. This also involves handling macOS keyboard-to-app layout mapper not reacting to this event as the window loses its first-class citizen status in this mode.
The others do sound useful too -- I personally hit a lot of spurious "tab output indicator" notifications in iTerm2, but if it _did_ work I could see how giving it up would be painful.