There is a difference between sheaves for wire rip halyards and rope halyards.
Because the diameter of wire is different than rope, the sheave reflects that difference by two different widths ( an inner and an outer) of grooves. A rope sheave is only one width or groove.
You can try to modify the wire sheave to a single diameter groove. Or it is better to replace the wire sheave with a sheave designed for rope.
if you desire the properties of wire in a rope, look to using Dyneema rope rather than polyester rope. Dyneema will be near zero stretch. Polyester will stretch 12-15% At break. 3-5% at normal load.