A puppet theatre I've been stalking a little bit. They make giant backpack puppets. This is a little old, I think they use Warbla now instead of papier mache. But either way they start with I'm guessing WED clay.
I ripped this from Caroline Thomas' instagram (@c_to_the_line) workshop with Andrew Kim
"Day two of @whatchamapuppet building our lantern puppet under @thingumatheatre ‘s tutelage. Yesterday we sculpted our head out of clay. Today we wrapped our head in plastic bags and cut out a pattern. After labeling, we transferred the pattern to a sheet of @worbla . Worbla is a thermoplastic that is malleable when heated and cools to a firm plastic. It’s also transparent, which is perfect for our lantern puppet. Each piece is heated and placed back on the clay head, carefully securing each seam with additional heat. The end product is a lightweight, paintable, transparent replica of our clay sculpture."
the trick with Warbla is the pattern will be exposed in the final product, so consider that.
Then they used Mulberry paper with watered down wood glue for 3 layers on the body. 
oh, found another team, A Blank Canvas. Looks like this one uses thin strips of foam (some type of Eva probably, seems like this stuff is all cosplayer roots)
Thingamjig had a cool dog sized frog. It would be awesome to make a light parade, A blank canvas does light projections on the street. So I can see a parade of people w/ jellyfish, and glow in the dark paint painting on audience getting them involved, and light projecting on the ground and surrounding buildings, bringing the whole world into the performance.
(or A blank Canvas style last unicorn play)
