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Verne,
I'd be afraid to sand the cardboard. I think you'd end up with a suede finish. These panels are pressed paper and their smooth finish comes from the rollers they are fed through. I seriously doubt if you could ever reproduce the smooth finish again without soaking the surface and running it through a pressurized roller system again. (But I've been wrong before.

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Has anyone tried painting them with different stages of gloss? Mine appears to be somewhere between a satin and semi-gloss finish.
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I'm sure it would be difficult, if not impossible. For all we know, the supplier might have painted sheets with a roller before die-cutting them out.
I agree that the original finish (paint or dye) had virtually no gloss to it at all. Just a slight sheen. Maybe a top coat with very low gloss paint & lots of thinner to blend it in might work? I'm going to have to try something on the blue package tray in my '62.......or just leave it original (faded).
Verne