I'm only guessing since I haven't done this before, but maybe try thick chunks of craft foam? That would be easier to sew on, I'm thinking.
Finished: Armin Arlert, Mayoi Hachikuji, Tomoko Kuroki, Ultimate Madoka, fem!Masky
In progress: Kougyoku Ren, Lightning Farron
Upcoming cons: Sabakon, Youmacon, Con+Alt+Delete