> Maybe you can enlighten me, it could be that I just did not discover the right tricks:
> Using "minimize" as a quick, non-distracting way to say "I am done with this window, I don't think I want to look at it again but I don't want to close the application just now because I may have to revisit the case".
I tend to middle-click the window title bar, which sends that window to the background.
You can also ask to have the minimize button back with GNOME Tweak Tool.
> Flipping windows on and off (I do this often for visual comparison of two near-identical graphs or images)
And a quick Alt-Tab or Alt-` doesn't work for this?
For images I prefer to do the comparison in my web browser: two images in adjacent tabs, fliping between them with Alt+number (or Ctrl+PgUp/PgDn, that's a bit slower).
> Selectively closing windows when a certain sub-task is done.
The overview is fine for this, if you can distinguish the windows visually. Which you already said you can't always, so disregard this part of my comment.
> That Gnome Shell is "great" with external displays is plain false.
Yes, multiple displays only work great if you position the desktops side-by-side. They don't work well if you position one of them above the other.