What material are you're bezels made out of? I work for a sign/printing company. To adhere most media types to foam core, we use 3M spray adhesive. Don't bother trying to use it on the MDF though unless you seal it first. The MDF will soak up most water based adhesives like a sponge if it isn't sealed or painted. Another option would be contact cement (like what is used to adhere melamine to MDF or particle board). I wouldn't recommend it for the foam core though, as the solvent will melt the foam if it comes into contact with it. I can grab a can of the 3M spray adhesive and get you a part number for it if that would be helpful. It's the best stuff we've found in 60yrs for mounting to foam core.
I'm on the other side of the pond, so I can't help you much with locating where to buy anything....