boat upholstery backing

Hi guys, I’m stuck on what to use
I have some rear seats moulded into the back of my boat and need to make an exact inner shell to support the foam and vinyl
This is my boat

This is what i want to end up with

but it has to be rigid enough to hold the sponge foam in its shape but soft enough for the upholsterers staple to go in without cracking or falling out, there will be a lot of staples in a line which may weaken a hard substance .similar cosistency to ldpe or chopping board or even like plywood.
If it wasn’t curved so much I would use ply