Phil, it's actually not uncommon to have frayed, door damaged and even dog chewed seatbelt webbing replaced. A local auto upholstery shop should be familiar with doing this and even have standard colored webbing in stock (esp. black). Local body shops will likely also know of someone local capable of doing it. A bit of research should soon show you it's really not rocket science, just something many of us aren't familiar with as it's not a common issue and generally not considered a DIY project as it requires a decent sewing machine and bit of sewing skill.

You can source your own auto seatbelt webbing online, which comes by the foot in a wide array of colors. Almost any place with a heavier duty sewing machine and familiar with doing thicker materials should be able to do a proper job. They need to use a decent weight of standard multi-strand poly thread so it's reasonably strong and won't decay. Mostly, it's just following the original double-stitched criss-cross pattern at the ends. The stitching pattern is where most of the strength is. With a bit of effort a household sewing machine could also do a decent job. There are a number of online videos, but this is where I start drawing the line as not many of us would have that kind of sewing ability and experience doing thicker materials, which includes me.

Going for used seat belt assemblies may be an adequate replacement option, but for some makes and models they may not be readily available, even new. Re-webbing and possibly needing to recondition the retractor may be your only option. Of course 30+ year old sun damaged and aged seatbelts are likely well past their best before date, so re-webbing may be a better choice even if it's a few dollars more. There are places listed online who specialize in checking and repairing the retractor as well as doing the webbing.

Automotive seatbelt webbing is almost all standard 2" (nominal 2"=50 mm, manufactured to a width of 47+/-1 mm, ISO min width for auto webbing is 46 mm). There are international testing standards for tensile strength, elongation and durability that vary by application. Thickness for auto applications is fairly standard so it's sure to retract under typical spring tension.

Most webbing sold as automotive seatbelt webbing should be adequate, but do try to source from reputable manufacturers/distributors. This is a case where going for cheapest may not be best the best idea. Ideally the webbing will be listed with an ISO or other testing certification, if not you can always ask. There are different requirements and testing standards for industrial applications, such as used in heavy equipment, and for that you might want to see some kind of proof the webbing is certified to those higher standards.
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Dave -still with 940's, prev 740/240/140/120 You'd think I'd have learned by now