Pivot Shoes identification
Hello,
I agree that the 15-179 would be our closest match to your pivot shoe but note that the depth only includes the housing, not the metal cam. The width also appears the same. The manufacturer will often round the measurement to the nearest 16th" since 59/64" would be difficult for customers to measure. Just let us know if you have any other questions and thanks for posting!
You should be good to go as long as there is no debris in the track or other damaged parts. One note I would make is that the black tip S600-29 spiral balances support a particularly heavy sash between 31-40 pounds. Make sure to confirm your window falls within that range and the housing tube has the same 5/8" diameter. We generally recommend silicone spray as a lubricant for jamb liners.