I don’t think the Rigid Dynamics analysis can do a flexible cable making frictional contact with rigid parts.
I know that a Static Structural analysis can do this.
It is important to put a generous blend radius on the edge of the hole where the cable comes out. It is much easier for the cable to make contact with a surface than a sharp edge.
The rest of your model description sounds good except that I would add a Joint load of type Force on the cable opposite to the one that has a Joint load of type Displacement. This force will provide a normal force to hold the two rolling surfaces together.
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