You may have already thought of this, after you have found the foam, its cut and in place. What I have found that works in my layouts, to keep the foam in place and to take away all noise. Is that spray foam that you use around doors and windows.
Don’t buy the max, but min expansion, and test it out first. A good friend of mine had the bright idea of filling his plastic decoys with the max expansion foam, the decoys split in half. I laugh so hard I was crying, he wasn’t he was PO big time.