Fantasy precedents say that when a badge of office is destroyed, it's a comment on the unworthiness of the officiant, and not some associated body For example, Saruman's staff ('line'?) in Lord of the Rings is broken as a comment on his own moral failings, and not, say, the Council that Saruman the White used to head.

If the enchanted stone that the Line is made of is subject to Harry's power of partial transfiguration then instead of breaking the Line he could take a piece of the chamber and make it into a new Line for himself. 'Merlin's spirit and Magic itself have endorsed me, now actually LISTEN to what I have to say.'

ETA: Or, since a few months ago in Azkaban he had enough power/skill to make quite a large hole in the walls and he's presumably improved further since then, and still assuming that partial transfiguration isn't one of the things the special stone is protected against, he could reshape a portion of the wall to say "Release Her". 'The stones themselves cry out against the injustice of this!'