How far could a Libertarian "judge" carry that? Carte blanche?
No further than a judge can carry judicial interpretation now. The forms of libertarianism that I have found compelling have not argued for any dramatic change in the manner of operation of government.
If you are talking about Supreme or Appeals Court judges, I would think they would still be bound by the Constitution; I have never heard of a libertarian arguing for anything else.
They argue little else.