It will not be possible to store each piece in a separate layout. Here is what I usually do when I need to randomly generate a level from pre-made scenes:
I put all scenes on the layout, somewhere outside of visible area. Scenes (yellow rectangles on the screenshot) have 'type' instance variable defined with values like 'easy', 'medium', 'hard'. This allows to build levels of different difficulties, and mix and match them, for example 5 medium scenes + 3 hard.
All objects on the scenes are added to one or two big families, in this case "Entities" for sprites and "Obstacles_TB" for tiled backgrounds.