I want a widget that will sit on top of the entire application. When I have tried to do this with Overlay.of(context).insert the overlay would later disappear a
Have you tried to add a Navigator as a child/descendant of your Scaffold? As far as I remember, the default navigator is in the MaterialApp, which is above everything. When you add your own Navigator, your routing will happen under the Scaffold rather than above it in the tree.