While the rendering took place I changed some of the interactive editors of the polyhedron. It is now possible to use a selection rectangle to select faces, edges and vertices for the creation of the next modifier. I missed it today when I tried to create one object for the upper ledger. I created two object pointers to use the small rectangle with the hole, put them a defined distance apart (I need that distance later) and then created a union of those two objects.
The next step was to remove the faces where the pieces are to meet. That all went very well. Then I need to push one of the small objects so it touches the other one exactly. For that I need to select all the vertices of that part of the object. Doing it by selecting each single face takes very long and is error prone. So I decided that the time to add rectangle selection is well spent.