If you’ll be keeping the original transverse bed layout, adding any additional thickness will shorten the already shortened bed.
Foam is a much better thermal insulator than Reflectix (which is meant to be left exposed as a radiant barrier). If the furring and foam are solid, smooth, and gap-free, I’d be inclined to leave it and put a finish layer of marine headliner (like Scamp’s rat fur) directly over it. But any bumps or gaps will show through the thin headliner.
Leaving all that wood inside the wall could mean trouble down the road if you have leaks
in any of the windows
or vents. A full resealing of everything now and ongoing maintenance will prevent that. What you have is similar to what Bigfoot
does, so you’re in good company!