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Ours slid a bunch, we use the 1/2" stuff, and had to milk it and burn it. Hasn't moved again. Definitely moves more than say stable braid, but the shock-absorbing qualities make it worth that little detractor.
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I can't help but think that removing the milked cover will reduce the amount of cover that is there to help absorb the shock? Nylon stretches more than polyester. It might be there deliberately to stretch with the core fibers. I don't own any Polydyne, nor have I used it. I have used Atlantic Braids "Husky" ropes, for many years, which have the same cover/core fibers. I have also used and own, Samson Ropes Amsteel 2 and Atlantic Braids Pro-Force, Polyester cover/Dyneema core. Haven't experienced milking on either product.
I would recommend calling either Sherrill or Yale Cordage. Keep all the cover you cut off, just in case.