I didn't see your previous thread and can't tell much from your pic above, but I'd be surprised if the pads are hardened. Seems unnecessary in a low-wear application like this, and usually a hardened surface will not grip as well as a softer one. And normal design practice would be to make the replaceable pads softer than than the more valuable cone on the main piece.
If it were me, I'd have a go at filing the tips of the clamping pads to match the shape of the cone, and make sure to round off any sharp edges that might dig into the cone. If the problem persisted, or if the pads were hardened, I reckon I would be making brass ones to fit.
Unless there is some specific reason Myford would make these pads hardened?
Edited By Hopper on 28/01/2018 06:16:10