yeah that makes sense. I suppose they could be glued to thicker card board or laminated. Nah laminated won't work, when you cut it they separate again. I wonder if they could be glued to balsam wood. That comes pretty thin, but card board would be just as well and cheaper!
I wonder if you coat them with lucite or acrylic? Either would make them water proof at least. They might react with the ink though and blur the images. May be I can try that on some worn out pieces for you... once some where out that is. :-)
We could try it on a new one... It just takes 5 minutes to fold one together.