Rose Vine Keepsake Box

This was a project that was an experiment that sort of went wrong. I tried for the first time to take a scrolled inlay pattern, then fill it in with polymer clay and bake according to the instructions. At first I was very pleased with the results, then I looked closely. Yikes! The lid now has a serious amount of cupping (last photo). Thinking about it later, I realized that heat removes moisture quickly which makes wood do strange things. I’m trying to think how I can straighten it out. Of course the topic of warping is as old as woodworking itself. The method i’ve tried before, with moderate success is wetting the concave or cupped side, then applying gentle heat, such as a hair dryer. Unfortunately, i laminated a thin piece of basswood to the underside of the lid to hide the rough underside of the design, so the glue would prevent the added moisture to penetrate the cupped side (I suppose I could simply remove the basswood by sanding), but a less destructive way would be preferable.
Anyways, any thoughts,opinions or suggestions are welcome.
Thanks,
Woodreamer

-- Bob, BC, Canada http://www.etsy.com/shop/abby702