I have a sculptor friend whose husband is a surgeon. She brought me a whole mess of medial casting materials (wrap and sheets) that cure simply when dipped in water. We messed around with it a bit in the studio. These materials can be purchased in various thicknesses, and strengths. The sheet material was approximately 1/8th inch thick and had holes punched throughout (I assume to help with the curing process.)
Yes, it is likely that this stuff can be used for reinforcing stuff, but you will first have to solve the little issue of your pepakura patterns being made of paper... otherwise you're going to just make a soggy mess.
The other problem in my mind about using this stuff for making Halo armor is that it is more expensive than resin by weight, and typically has to be special ordered via medial supply houses. Most people seem to balk at finding the right supplier for their casting resin/fiberglass... which is a whole lot easier to find than retail medial casting supplies. I think unless you've got a Doctor in the family, finding this stuff cheap and easily could be the next biggest hurdle.
The other thing I recall from working with it is that it adds bulk, more than strength... that is that the bulk it's adding kinda exceeds the strength it adds. You'd loose significant detail... which you wouldn't be able to carve into the porous material... it would need to be added ontop.
It might be something to explore, but I wouldn't invest too heavily in the material. Go with something tried and true. Don't like the toxicity? Use Aqua-Resin instead.