Short of writing a script. Is there any default blender-native way of adding aspects of the scene into the render path name?
Im thinking something like
//some_directory/{layer}/my_{scene}_{layer}_render.####.ext
would replace all the sections with {layer} with the layer name ( i know this wouldnt really work if rendering multiple layers into an exr etc but i mean the general gist of this) and of course {scene} with the scene name.