I think there is a matter of physics that is addressed in the video mechanism, that 16 servos will need to accommodate in software.
The large tangential rotor in the center of the 'driving' wheel on the left in the video - converts the rotation into a smooth sine waveform.
Each servo will have either a horn, or pulley that tugs the individual strings. There's your problem. Speed of the string at the center of the servo arc will be faster than at the ends on axis with the string line.
I could be wrong, but that's what I'd be looking at.