So here it goes. I cut two dowels into shape and attached the first of 12 pieces. You can see it is already quite thick. And it does have some spring to it, but when it has been held in shape for a while, it should settle and not spring open that much. Actually this effect could be observed pretty much right away.
I attached it to the dowel with the help of some staples and glue. To make sure it stays in place while the glue settles, and to let the Tyvek adjust to being rolled up tightly, I wrapped more paper around and closed it off with some tape.
Next up is attaching the next piece.