I've used 3/16" foamcore mouthplates in puppets with much success. As detailed in the excellent book "The Foam Book" from Grey Seal Puppets, the foamcore is treated in such a manner as to reinforce it to stand up to normal use.
I hadn't thought of using the corrugated plastic, which is ironic since I work in a facility that has a sign shop. Incidentally, this could prove to be an excellent resource for coroplast. We frequently have scraps left over from signs that are not big enough for other signs, but would certainly be sufficient for most mouthplates. Get to know your local sign shop!
Another mouthplate idea. For a softer, more pliable mouth, go to your local print shop. Ask them if they have an old blanket from a printing press. These are what actually press the ink onto paper, and are made with a neoprene surface with a heavy fabric backing. They are thin and extremely durable.