has used RayFoil (like Reflectix) behind the marine headliner since 1985, and it lasts for decades. Just use the right adhesive. 3M90 for small areas and auto headliner adhesive for a whole trailer installation.
I agree you’ll want something better than thin canvas over it. Even if you use a synthetic canvas, it will show every bump and wrinkle. Have to say, marine headliner is a great product. It’s available from a number of suppliers in a variety of colors and textures. Unlike carpet it has no backing, and it’s slightly stretchy to fit the curves.