Starting with the easy answer- for attaching or laminating foam, use 3M Super 77 spray adhesive. You can get it a big box office supply stores and box home stores.

If I were going to attach the mushroom stuff the first thing I'd try would be 3M laminating film, but that's because I've got a pile of the stuff. It's very thin material with very strong adhesive on either side, kind of like double-stick tape. It's pretty reversible, which means it's also easy to redo if it fails.

Otherwise you might try using West Systems G/Flex epoxy. They did some destructive testing for Epoxyworks magazine with D-rings attatched to plastic canoes, and the bond was stronger than the material, and you won't need that kind of strength for this. I've had pretty good results using G/flex, but I have a friend who has used it a lot more than I have who has gotten very good bordering on excellent results. I'm sure for this project it would be worth a try. It's very thick stuff, but if you don't add cab-o-sil it will run, and that's a mess. I would tape off the area around where the mushroom stuff will go, scuff up the back and glue it on. To hold it down evenly while it cures put some sand in a bag and lay that on top. It will be weighty and conform well. Take it off as soon as it starts to cure so cleanup will be easier. It cures a lot slower than West's other products. You can attach the mating surface to the foam with Super 77.

If you need to/want to remove either the epoxy or the spray adhesive heat will usually do the trick, followed by an adhesive remover like 3M's General purpose adhesive remover for any residue.

I don't think you should use 5200. It's permanent permanent, not permanent like a sharpie marker is permanent.

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