The guys at my local homebuilder's association use some glue to bond wood to foam, foam to foam, and even foam to wood. They call it "polyurethane glue". It is found in hardware stores, as an exterior wood glue. They also use it to "glaze" the exposed face of the foam. One of the builders did his entire aircraft with it, as a substitute to Epoxy. He says he made some tests, proving that the pond was as strong as Epoxy.
Haven't tried it yet. Serge Vidal KR2 "Kilimanjaro Cloud" Paris, France