look for something that is used commercially for noise dampening and then you will also be able to find something that will have fire retardant qualities.
You could use silicone sheet gasket material, it comes in various thicknesses…
Prolly can manage to cut it and fold it around the inside corners. Adhere it with black RTV silicone sealant and use the rtv to pretty up the corners and anything not easily covered with tsheet.
Then go over the whole lot with spray on or brush on bed liner.
These were the guys when I was sound proofing my van. They did a thin,(1-2mm) self adhesive rubber sheet that was used in dampening vibrations from car body panels. I phoned them up and they were very knowledgeable and helpful. They even sent out the product before I paid for it.
It’s extremely sticky and follows shapes well.