Read the article: hackaday.com/20... [David] and his brother [Jed] recreated this braiding machine from an 1890's machine they found in a surplus store. Endslate Audio: Indigo by Kodisha / indigo
Good work David and Jed. You need to keep the braiding point under control, so it needs to be constrained within a loose die or hole. The braiding point should be at a 45 degree angle to the vertical, and the pull-off of the braided cord should be speed controlled to keep the laying point at this die position.
Just found this video -- thinking that the crank can work on a ring gear, with the "odd-numbered" cogs having gears that drive from that ring. This way, you don't have the furthest cog having to be driven by all the others. Also the crank wouldn't need the large driver there.
Litz wire does not have to be braided (rarely is) it is just a very large number of individually insulated strands covered all over. Often the outer covering was silk thread, wound around possibly in two opposite direction layers. Overall braid might be nice but not needed for function. This could be used to make custom coverings for electrical cords to personalize or protect them.