Use contact adhesive to glue your originals to a new backing.
I’d use waterproof panel board, not suggesting a supplier but here’s what it looks like.
https://www.perfectfit.com/15347/15...ard/Kraft-Tan-Waterproof-Panelboard.html

If you need to tune up your old panels first I wonder if a steam iron and a fabric blotter to protect the original surface might help, I’ve not tried it?

•1951 GMC 250 in the Project Journals
•1948 Chevrolet 6400 - Detroit Diesel 4-53T - Roadranger 10 speed overdrive - 4 wheel disc brakes
•1952 Chevrolet 3800 pickup
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"First, get a clear notion of what you desire to accomplish, and then in all probability you will succeed in doing it..." -Henry Maudslay-