Bigfoot uses a spray contact adhesive. You want something that is somewhat resistant to softening with heat, and with solvents that do not melt the foam. Given that there is probably residual contact adhesive on the fiberglass, using the same type of product might be advisable as other things may not stick well to it. Silicone would be near the bottom of my list, it is not a very strong adhesive and yet will be hard to clean out it if comes loose, nothing at all stick to it. When boatbuilders use foam core, they will mix polyester of epoxy with fillers to thicken it, then use a notch trowel to apply.
Blue foam (extruded polystyrene) is a better choice for a core material than bead board (expanded polystyrene). I don't know why Bigfoot changed - XPS is less expensive I guess.