Sagging headliner

Thanks, everyone. I wrote Winnebago, too, and got this useful answer this morning: "We have seen instances like this where the headliner adhesion has let loose. Unfortunately, the only way to make a proper repair is to remove the old fabric and glue up new fabric or just replace the whole panel with the fabric already glued to luan paneling. This can be quite the task depending on how much fabric is coming loose from the panels. Depending on where and how much it is falling, you may be able to secure it using batt strips, upholstery tacks or rosettes. Those are just a couple of options that we have heard other owners doing."

This implies that there is something up there to which I can attach screws/tacks. Well, that'll be another fun project, unless I succumb and let an upholstery shop invade my wallet.