This is the result. Our bed is covered with the 3×4 (doubled) 0.5mm PVC sheet I bought in Hornbach (see this post). I think looks quite “professional” ;-) And for €21.
After I unpacked the sheet, the first thing I did was rolling into it like a mummy. Back were those times when I was 12-14 yo ;-)
The original smell was quite strong and despite an open window I had to cover it with a latex sheet for the night. After ~30hours the smell was bearable and yesterday I spent my first night on 1mm PVC bedsheets. It felt like thick smooth chlorinated latex, a bit too firm to be comfortable, but still OK.