Well @bocaholly, everyone knows that engineers are kids that never grew up.  I bought loads of Radio Shack T Shirts when the company finally went out of business for $2 each.  I have a bi daily alternation with a Simpson “I dress myself” shirt so people will not reach the conclusion that I have worn the same shirt for five years running.

Hi @steveduf and others.   I have spent some time looking at videos.   If you have access to a table saw and perhaps a band saw, I think it possible to make your own binding.  I would get a thin kerf 8 inch diameter skill saw blade to waste the smallest amount of wood possible.  

Select boards of species reflective of existing rope element colors (assume maple or birch for light and cherry or walnut for dark).  Rip to match height of existing binding.  Plane or sand top and bottom surfaces to finish dimension.  Dye to match existing binding.

Tilt table saw blade 45 degrees (or to match existing binding) and use veneer jig (easy to make) to produce rhombus ended sticks of about 4 inches in length.  Glue up alternating sticks (avoid gluing end surfaces) starting with a dark stick and ending with a light stick and compress between wax paper.  Cut to required width on table saw or band saw.  Extend length if necessary using glue.

Another photo.  I still think it could be done.

You might want to look at Harbor Freight item #61608.  Provided 4 inch saw blade is useless, but a suitable carbide tipped blade is inexpensive.  Once veneer is created, slicing “tooth picks” can also be accomplished with a fret saw if angle can be established with a guide block.  You might also look at making a planing guide similar to that used in making split bamboo fly rods.  We can do this without you going blind in the process.