Hi digitaldave,
It may not fit inside the cover or the fire barrier (or if it does it may be more compressed or “squished” which can change how it feels and performs (see posts #3 and #4 here and this topic about the differences between a layer inside the cover and outside the cover).
I would at least start with the extra layer outside the cover for the sake of “fit” and simplicity but in the end the one that works the best for you would be the one I would use. If you do decide to try it inside the cover (and assuming it “fits”) I would tend to use it over the fire barrier because it will contour a little more effectively than if there is an additional layer of non woven material over it.
Phoenix