Jesper sent me a message today with the details of the product he proposes to use: the Mataki Självtäck 5000 (which sounds like a Japanese robot to me).
Självtäck translates as "self cover"; it's designed to be easy to roll out and glue together. The '5000' version is much thicker and is designed to be used on roofs like ours with a shallow pitch.
I'm waiting to hear Anders' new price for a paper roof, and I want to talk to Janne, too, before I decide. But the clock is ticking; the roof really needs to be done within the next 6 weeks.