How to set Super/Windows key to Show All Applications menu in GNOME DE?

Not sure why you couldn't get it working with those dconf settings. This works for me (in Ubuntu 18.04):

gsettings set org.gnome.mutter overlay-key ''
gsettings set org.gnome.shell.keybindings toggle-application-view "['Super_L']"

In my case I needed to figure out which key was mapped to the physical super key.

1. Launch Settings -> Region & Language.
2. Click on the Input Sources list and choose a language (in my case it was English).
3. Click on the little "keyboard" button in the right corner of the window and launch "Show keyboard layout".
4. Click Super button and figure out that it's mapped to Super_R
5. Run gsettings set org.gnome.desktop.wm.keybindings panel-main-menu "['Super_R']"

All good now!

I configured those keys directly through Settings -> Devices -> Keyboard on Ubuntu 17.10. Under "System" section you have "Show the overview" which you can disable (by pressing backspace). And for "Show all applications" you can configure then Super.