This is not in my wheelhouse of experience, but based on the engineering mechanics of things, can you cock the star nut by holding under one side with a hook or one of those tools that looks like a small icepick with a 90 degree bend in it, then push down on the opposite side, until the nut is on edge to the bore axis, then hook the center hole and extract?

Regarding damage to a carbon steer tube, if damaged, I would think, it should be evident in fracturing of the resin?