Spray77. Tape off the painted surfaces so you can get right up to the corners on the lid. Spray the fiberglass. Wait a minute, spray the back of the carpet (because the glue will set up faster on the carpet than on the fiberglass.)
As soon as it's "tacky," i.e. It's still sticky but the glue stays on the surface vs sticking to your finger when you touch it, mate the two surfaces.
Have a helper, you only get one shot at it. If you have to take it off and redo it, the bond will be much reduced. Have your helper hold the lid so you can press on the carpet. Like you're ironing it. 3-5 minutes will do it.