This is better than the previous design but the pulley is just too small.
Here is an idea for preventing damage to the wire. Doesn't function as intended with wire rope stop sleeves.
This sort of works, but requires a constant tension to keep from unspooling. Testing and/or mathematics will be needed to determine if attaching a pulley to a servo is beyond the mechanical limits of the output shaft.
The idle pulley design works well, but bearings with a 3mm bore are way too expensive. The next design will test bronze or teflon bushings for the idler.
Here a stop sleeve that is one size too large has been ruthlessly swaged on to the wire rope. Perhaps epoxy might be a better method for seizing the end of a wire rope that is 3/64".
Unfortunately, it looks like 3/64" wire rope is still too stiff to be wound on a 38mm (1.5") pulley. It does not lay flat on the pulley and has a tendency to unspool. Braided fishing line looks like an alternative.
It looks like wire rope won't work for the original concept, perhaps it will work on a 76mm (3") pulley. Testing with this design showed that the wire would come off after the first layer due to a design flaw.
This looks like it might work better.
However, there are still problems with the initial lay of the cable. While it may not be a problem for limited cycles, fatigue at the starting hole will likely be a problem.
This looks like the source of the problems.
So, here is another fine assortment of design failures on the road to success and robots with tentacles.