Using sheetrock 1/4″ for the ceiling was something I was hoping would work.
Today we (My sister Petra and brother Arne arrived yesterday) tried, and luckily it does:

Putting up 8×4 boards is really impossible without help, but with 3 it’s easy.

Except for a little strip at the back and the window, now all walls and ceilings are insulated and covered.
It looks cosy and will be easy to cool/ heat as it’s less cubic feet. When all strips are in and the beams are stained it will look nice.