If you would like to use material that is similar to the headliner cardboard, I would recommend calling Classic Parts. They carry a headliner kit for the Suburban. I ordered a kit from them and in the process discovered that one of the pieces had been cut wrongly. I called them and they were able to send me an uncut piece from their supplier--they may be able to obtain pieces of this material uncut, which you could then trim to fit your panel accordingly. It might be worth a try.

Good luck!