to change various things in a properties of a model’s objects, such as paint color, whether an object is hidden, an object’s size/location, etc…
Generally in SketchUp the geometry must be created or modified for different conditions like these, excepting the visibility, which can be controlled by use of layers (and you set which layers are in a visible in a scene). With dynamic components one can change a number of these things for different scenes. Also there are animation plugins like Fredo’s you could look at. But you are correct, “Scenes” in Sketchup mostly control style, shadows, fog and camera, and layer visibility–but you can choose e.g. which state of a dynamic component is displayed.
I suspect, without further knowledge of what you are trying to do, that simply rearranging and re-texturing different copies of your geometry (only for those components that must change) would be the easiest and fastest way forward, for that part. Then you can choose which version you want to show in each scene. It seems to me this gives you ultimate control, while still keeping everything associated in one file.