I dont remember the Biscayne doors off the top of my head but here are a couple of things to remember. In the early 60's a technology came into place called Di-electric bonding, other wise known as resistance welding. The process was used to "burnish" vinyl or cloth so that is had the appearance of sewing where it did not or to install a logo or theme line. The process was used up until the late 80's until insert molding came into place and non supported vinyl molding and slush molding was perfected and replaced it completely. The only place the technology is still used is installing clear vinyl on production soft tops. And seat belt boot molding on some rare cases. The other place you see it used is on marine vinyl "pleated" roll goods that have simulated fales to prevent water encroachment.
If your car has this type of thing on the doors very few have the equipment to produce this operation. Typically,a rare few marine top/trim shops may have it for putting in logos or windows.
The process requires a press that applies pressure and current (producing heat via resistance) to the material along with a specialized die to create the pattern. Luckily I had the chance and purchased one of these machince along with a pretty hefty set of dies for everything from the mustang logo to fake french seams. There is not alot of call for this stuff now a days but I use it from time to time.
Your best bet would to try to find a reproduction shop or find the best pair of used ones you can find and die/paint it. If it is not a dielectric job a good pattern maker can reproduce it but it would probably cost you a lot to get a good job done. I agree with the above post from Goth that there are quite a few of us old school guys that know how and are willing to make them. But to do them "right" will cost a bit more.