If getting screws to bite in XPS foam isn't working, install some drywall anchors. They look like super-fat wood screws, the threads are about 1/8" deep. That should hold pretty good.
Better still: set the anchor, back it out and shoot some Gorilla Glue adhesive into the hole, then set the anchor again. Let the glue cure before installing your screws. That should hold VERY well.
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Lead or follow. Either is fine.
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