I'm working on a project - not theatre specific but I believe similar materials and processes to scenery - basically building a stressed skin panel with extruded polystyrene (XPX) cores and plywood skins. So far, it seems that 3Ms Fastbond 30NF is a good option and it's available from sources that I can order form and in quantities I can use. (I found some others that might be superior but they tend to be in drums of on pallets, and not set up to sell to a one project DIYer). It's basically a water based contact cement that won't dissolve the foamed plastic and provides a bond that is at least as strong as the "polystyrene tear strength", which I assume means it's strong enough. I wondered if anyone here had experience with this product and application.