Answer
Hmmmm, looks like you've covered all the bases. Foamcore board is hard to cut because it blunts blades so quickly. The solution I've found is to use cheap craft knives with the snap off type blades. Styrene is available in pre cut blocks for wargamers, in various thicknesses online. The old railway modelers staple, paper mache or plaster bandage over chickenwire, can be really messy. There are a few things you can use from the sign industry, if you are doing corridors etc, Foamex, is similar to foamcore, but much denser, cuts like wood only easier, and can be sanded and screwed together. There is another product, really pricey which is an ultradense styrene, which you need a power tool to shape, but I dont know its name, sorry