This gnome-shell bug report both outlines the problem with Super+Key shortcuts, and details a hacky workaround (which completely fixes the problem for me!):
Basically, the issue is that custom shortcuts are handled by gnome-settings-daemon, which does not pick up the Super key properly. The window manager (in this case, mutter) can see the Super key. So, Olivier Crete wrote an extension that reads your custom shortcut definitions and passes them up to mutter. I installed the extension and it works great for me. No double key pressing needed like some of the previous commenters were talking about.
The extension is not in the official gnome extensions site because it was rejected (you can read the hilarious reviews over here: https://extensions.gnome.org/review/1658 ... apparently the reviewers are having problems with reading comprehension!). However, you can download the extension via comment 33 in the bug report.
Unzip the file to your ~/.local/share/gnome-shell/extensions directory, restart gnome-shell (Alt+F2, r), and fire up Gnome Tweak Tool and enable the extension. You should then be good to go.
EDIT: One more thing. If you have more than 6 custom shortcuts and activate this extension, gnome shell will explode. The extension hard codes in support for 10 shortcuts, but only compiled support for 6. To add support for an arbitrary number of shortcuts, in the schemas directory edit the org.gnome.shell.extensions.command-keybindings.gschema.xml file and copy/paste more binding entires (it should be self evident how to do that- just make sure to increment the binding-#). Then, in the schemas directory run "glib-compile-schemas ." Finally, in the extension.js file, find the "for (let i = 0; i < 10; i++)" line and change 10 to the number of total bindings you set. Now you should have support for lots more custom shortcuts. Phew! No one said Gnome 3 was easy! Oh, wait...