I'd really like to see the cutter shape and slow motion to fully appreciate the process!
Well, as a start, have a look at this - is it slow enough?
Then, maybe replace the mechanical master templates with electro-wizardry.
What I did find very interesting was the brief system sketch at the beginning of the original video which appeared to show a cardan shaft betwixt the headstock spindle and the back of the carriage. I wondered if it could be simplified as effectively a copy lathe or even just a TTA but with a master profile which rotated in exact 1:1 with the workpiece, and then a follower which guided the tool (secondary power spindle?) in & out following the master?
There's probably a patent from the 1800s which has the progenitor for this, just driven from a line shaft!
Dave