Interior A/C filter cover

I own a Class A 2008 Fleetwood Excursion 40X. The cover over the rear A/C filter is affixed to the "soft" interior ceiling material with 4 screws in the corners. Over the years the screw "holes" in the soft ceiling material have worn to the point they will no longer take the screws. Longer screws proved fruitless. Larger diameter screws (like going from a #6 to a #8 for example) would require enlarging the holes in the cover and, even if this were initially successful, would eventually result in the same issue. The holes, again, would eventually wear. I tried applying Velcro squares (hooks) on the ceiling and wrapping corresponding strips (loops) around the corners of the cover. However, it looks like the adhesive backing on the Velcro does not stick well or long on the ceiling. I guess I can use contact cement in an attempt to make them stick better but that seems rather drastic at this point in time. Has anyone out there come across this problem? Have you come up with a fix? Any ideas?