The cable design looks funky! But I am still unconvinced by using an active system, I would be concerned about slippage, stretching etc..
Dont know if this will help but here goes........
The cable system shown looks like it is one continuous cable. I recently had the joy of repairing a Freelander electric window How ever the way it worked looked to be adaptable for CNC. (now the hard bit)

It used 3 cables. 1 connected the two slides together (via pullys) so they always stay the correct distance apart(i.e. anti-racking) each slide then had a cable going back to the motor. These were attached in opposing directions,(as one wound on the other wound off) In effect the sytem is only ever pulling and cant slip because each end is locked to the drive pully.

The only dificulty is that the distance of travel is governed by the diameter of the pulley and the width (no, of turns). If you increase the width to much then it will cause an arc and introduce an error.

If circumference = pi x D then a 100mm dia. pulley with only 5 turns on it the travel would be 1570mm (if Ive got that correct ) would probably need a belt reduction to the motor to get any reasonable power.

For a bit of stainless cable and a few pulleys its got to be worth a try