“If you need to screw something to the underside of the foam, just glue a 4 inch square of wood to the foam.”
Sure, that works too. That’s especially good if you need to prefabricate an assembly prior to mounting. Other techniques include just gluing the device to the foam, or sticking it in place with double-sided tape. There are lots of ways. I find that screwing the device directly to the foam is simple, it works and it allows me to easily remove the device. My main point is that you don’t need wood down there to mount things on.
george