What a great idea, SunRiseArts! I've used cardboard on either side of some thinner silicone molds and it's an iffy proposition when I do that; sometimes it works, sometimes it doesn't make much difference.
I think I'll try your wooden sticks method. I'll look for some tongue depressors because they are wider than pop-sickle sticks. So how did you attach the hinges? Do they have those tiny little nails? Or do they have screws?
How does the duct tape hold up with CPOP? I once used duct tape on a muffler of an old car I had, and it held for quite a long time, but eventually the adhesive gave way (due to the heat, I expect.) So I've never given much thought to using duct tape in areas that would be exposed to a lot of heat since then.