I do a lot of construction and repair with Beacon Foam-Tac. It's safe on all kinds of foams, doesn't have stinky fumes, dries quickly, doesn't yellow, and maintains a rubbery, resiliant quality. 
I broke off the nose of my F-22 yesterday, and thought I'd document the repair. EPP foam is great for this kind of disaster. I applied the Foam-Tac to one surface, mashed and unmashed the surfaces together, let dry for a few seconds, and made the final join.
In under an hour the joint is firm. I think the directions say to let it cure for 24 hours for maximum strength. As you can see here, it's nearly impossible to see the repair line.Here's a video of the process. Made with my new downshooter!
