Welcome to the forum.
On my 2000 380DA the padded fabric headliner fabric is attached to plywood. That plywood is screwed to fir strips attached to the bottom of the fiberglass ceiling.
The padded fabric is glued to the headliner plywood.
The plywood is screwed at select locations around the perimeter to the fir strips. The padded headliner fabric is NOT glued to the plywood at the locations where the screws are placed.
It is possible to feel the screw heads through the padded fabric by feel, by pushing into the fabric.
When a screw is located the headliner fabric is carefully pulled out of the seam to expose the screw head.
On my boat, in multiple instances, the factory placed several screws close to each other, about an inch apart. So if a screw is located, then don't assume the next screw is far away.
Note if going through that effort it would be a great idea to rebed everything that is exposed by removing the headliner.
Please report on results.