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Get belt webbing at some fabric wholesale warehouses. The shoulder belt webbing is the same width, but thinner than the seat belt webbing. However, you can use the same [thicker] webbing for both and have it work OK.
Take new webbing and old belts (still assembled) to a racing seat belt maker, upholstery shop (car or not), or other shop that has heavy stitching machines. They will reel the old belt out, cut off the old belt except for the last 4-6", and sew new webbing onto the 'stub' left on the reel. Since no sun ever got to that area of the belt, it is probably just as strong as it ever was...no problem with strength. The shop just needs to duplicate the same construction and stitching as came with the original belts.
And, if you can't find the correct color belts, just shoot them with SEM ColorCoat vinyl dye. Nylon is 'plastic' and takes vinyl dye just fine. They will recolor to match your interior color code with no problem. Dye the webbing before taking it to the upholsterer.
Designer Imagines A Corvette That Looks More Like a Corvette Than the Corvette
Slideshow: A Jaguar designer's personal project imagines what a modern front-engined Corvette might look like if Chevrolet revisited the golden age of the Stingray.