The old car uses some form of wood based fibre board for the door cards and the instrument cover. Both covered in 'leather' so look OK when new. The instrument covers would warp within a few years from new - but have been re-manufactured in fibreglass which solves the problem totally.
The door cards being a much more complex shape would be pretty costly to re-manufacture and given the padded 'leather' is also moulded to the shape, very difficult to make like the original. They don't warp as such, but the wrapped over front and back loses its shape and then catches on the door frame and can rip off the card if forced.
The usual trick is to make sheet steel reinforcing brackets and glue them inside the card, to restore the original side profile. But over time the glue simply lifts a layer of the fibre board.
What would be ideal was a glue which soaked into the fibre as much as possible. And if it would stick the steel and leather too, so much the better. Not a problem clamping things up until the glue dries.