How to stiffen flexible plywood
Laminating a second layer of the same product should stiffen it substantially. Once the first layer is positioned the way you want, spread several beads of construction adhesive across the face of it and conform a second layer over the first. Tack in place with brads using a nailgun to hold it in place until the adhesive sets.

Note: These flexible plywoods come in a variety of thicknesses. It is likely that the thicker ones will be somewhat stiffer than the thin ones. I realize that even the thick ones may not be rigid enough for your application.