3M 5200 Marine Polyurethane Adhesive/Sealant might also work. Just not sure how any of these suggestions would work with the foam core.
And to apply pressure to a vertical wall while the glue is setting might be a little tricky. Know somebody who successfully used sand-bags when repairing a Al-Al delam on his roof with 3M 5200, but you will need some sort of cross-brace for a wall.
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