Craig,
Tight Bond works well for bonding foam to foam but not so much for other materials to foam.
I use a Polyurethane sealant like Vulkim Seal to bond wood or metal (beverage can corrugated metal) to the foam. it is a little messy and takes a while to set/cure but holds really well.
Have had it outside 24/7 for about 3 years on my mill buildings with no problem at all. It is flexible and has a very secure bond.