In the end I gave up on learning to use global vertex and geometry shaders, but while looking for alternative solutions I found out that nDisplay’s Mesh Policy does exactly what I needed.
However if you want your scene projection to happen directy in the editor and without having to learn how to use nDisplay and Switchboard first, you can also just place a camera directly in front of a mesh whose texture is a render target of a Scene Capture 2D (which acts as the real camera in that case). I verified that the Scene Capture 2D is rendered before the main camera, so you’re not introducing a 1-frame delay this way.