Briefly submerse the binding stock in water before bending. Re-wet during the heating process if necessary.
Remember, it's not the water that allows the wood to bend. It's the heat.
The water (steam) carries the heat into the fibers and resins of the wood without scorching the surface of the wood. As the resins soften from the heat, the wood fibers can slide past each other... the wood can bend.
The .020" stock will bend w/o heating.
CAUTION: To build this rosette one needs to be able to glue up 13 pieces of wood at the same time. Each glue joint is more than a foot long. Keeping the glue under control is essential. Apply glue in thin measures and allow the glue to tack up slightly before wrapping it into the rosette and applying clamps.