I use 1/8" thick gasket rubber for flexible mouthplates. You can get it from Lowe's. For rigid mouthplates (like Scooter's) I buy a large plastic storage tub from Target and cut the plates out of that.
I pin the "skin" onto the head and sew it right on top of the skull using the baseball stitch, then gently pick and brush the seams to hide them. I sew the fleece "lip" to the felt covering the mouthplate as it is rather than turning it inside out. Some people think that's a weird way to do it, but it works for me.