craftgrrl | uncurving shrinkydinks?

The first batch of my shrinky dinks came out perfectly. The second, not so much! They're super curvy and would not flatten out completely during baking time after shrinkage. I tried the recommended technique of folded paper pressing lightly till it cools. No dice. I even tried placing it back in the oven before it cooled completely. Once again, no dice. I know there is nothing I can do about it now that they're cooled and solid, but I'm asking for future reference. Any tips from you lovely folks to prevent curving or aid in my quest for the perfect shrinky dink?

I never found wings for these puppies! So I guess they're just one-eyed one horned purple people eaters for now.
They have little claws that wrap up around my leg up to my knee. These pictures really don't do them justice.