Hey! ...Wow! ...that is a nice cabinet.
I love the rounded corners.
The cable slack problem could be addressed with a cable/weight system.
A pulley is located at the top of the enclosure, and on the inside. A cable is attached to the bundle of cables that has slack. When the Drawer is open, the cables will extend (there will be a mild tension from the weight).
When the drawer is closed, the weight sinks and pulls the cable bundle upward and clear of the drawer closing mechanism and any internal hardware.
The trick is to get the correct weight, length of cable, and the amount of slack that all cables have in an average that will maintain consistent stress-relief.
Again... really nice case. Not what I expected. I expected one of those clunky metal ones that one finds in most office environments (with sharp edges and angles). The desktop just finishes it off perfectly.