I've been thinking of a Rex cosplay as well. One of my early schematics is located on dA here
Even though you said you wanted to shy away from it, I'd say cardboard would actually be your best bet as far as being light, giving you planar surfaces, and being easy to work. And with your papercraft Rex, you'd just have to scale up the measurements and find appropriately large pieces of cardboard (try Costco or your equivalent wholesale place). As for waterproofing, I'm sure that if you use a good sealant, fibreglass, or possibly throw some glue-based paper mache on it, it would be sufficiently waterproof.