Yea 200 for a piece of plastic is stupid lol I make plastic for a living can get all kinds of plastic.
I wonder if a cheap piece of wall paneling would work for the backer?
No I don't think that wood paneling would work at all. A lot of times it's that fiberboard or whatever and it's not pliable enough. It would snap I think and it's too thick way too thick.
If you got access to different thicknesses of big sheets of plastic than definitely you've got a good material. I would absolutely try that if I had it.