When I was doing my Greek mask project, I accidently stumbled across this video about making traditional camel skin lamps in Pakistan. it's not quite paper mache, but it's super close, and fascinating to see how they made molds that they could crack out of their lamps.
It's basically like they're making a paper mache made with skin, (I'm assuming) gelatin glue, and plaster of Paris.
Their plaster of Paris is likely taking the roll of our balloon. White the skin=paper and the gelatin = glue. They even make a "paper clay" with ground up camel skin!
Since the lamp is made of skin/leather and (I would assume) gelatin from the skin, it's strong enough and flexible enough that you can bash it just hard enough to crack out the plaster of Paris without hurting the lamp. I think the same technique would likely break a paper mache mask made with wheat glue. My student with a wheat-glue mask had a fragile mask that cracked easily.
I honestly think a similar method to this was used to make the Greek theater masks. They likely used linen cloth (this is before the invention of paper) or maybe leather, and likely a wheat or gelatin glue. Whatever they used, it decomposed, because there's no existing masks to look at.