I have found a way to make the roof fold-flat-able.
This is what it looks like assembled.
It is combined out of these two main components ...
The core part is the extension of the walls. I have decoupled it from the walls so I can interchange other 4x4"base walls however I like. It's function obviously is to hold the other module, the main, wide roof in position.
And this is what it looks like flat-folded...
Now it all fits nicely into a box or envelope for storage and transport. The only thing missing is some additional flaps to help position the outer roof into the core frame. And then I can start the texturing.
I want to more or less reuse the texturing from the Asian Bell tower but I have found that there are also shrine versions where on top of a wood shingle layer there is additional reed. So maybe I will make this as an optional texture layer.
In any case I am very happy I could make this work.