Sagging Ceiling

So, it is very evident that there is a seam in the luan that runs the length of the bathtub (front to back) that lines up directly with the hallway edge of the tub. There is a sag in that part of the ceiling and I am pretty sure that the only think keeping that section of luan up is the carpeted ceiling. So, I am hoping you can steer me in the right direction. (I am pretty handy.) Is there a specific glue that I could use to join the Styrofoam and luan together? I am thinking I may have to replace that piece of luan so I have new anchor points for the skylight in the shower. The other thing I am thinking is when I try to re-glue the luan; maybe just replace that with plastic panel (like a tub surround) and glue that up to get rid of the carpet in the ceiling above the shower.

1997 Winnebago Chieftain.