Snark-
Actually the green foam is a higher quality than the white/beige foam that one usually sees. I use it a lot myself. In fact, Garth 2.0 (my avatar) is made of 1" foam for the body and 1/2" for the head. Since I never use exposed foam, I'm not concerned with any "sheen" issues.
I have been very happy with puppets I've built from "The Foam Book" videos, and Gabe, (who can be seen at
http://home.mcn.net/~fantom/pages/puppets.html) has a mouthplate of 3/16" foamcore. Since it is all encased in other foam and fabric, it is well-protected against moisture, and has proved to be very satisfactory. But I too have used everything from plain old felt (see the original Garth at the above address) to gasket rubber to coroplast to sintra to neoprene.
The company I work for manufactures straps and pouches out of neoprene and they are kind enough to throw a few scraps my way from time to time. It's really great because it holds its form well, but is completely malleable when I need to "make a face". If you can find an old wetsuit at the second-hand store you can use that as a source for neoprene.
As has been stated amply here before, whatever works best for you is the best material to use.
P.S. I wouldn't worry too much about missing the 90 degrees on the jaw. You should be able to correct that with the neck covering. (When I am making patterns I glue up a paper pattern first to make sure I have enough material to make the 90 degrees.)