I don't understand why you'd want to make the Judiciary even more independent.
Because the current system allows for a partisan Judiciary. The Judiciary and the Justice Department need to be non-partisan and trusted by both parties.
The filibuster in the Senate helped somewhat. The minor party could protect itself from extremely partisan judges but Reid has removed that check. There is essentially no protection now. It would take a constitutional change to restore that protection.
And what can be done about Eric Holder? He's already been found in contempt of congress. He should be at minimum subject to a confidence vote.
The independence of Justice and Judiciary is impossible now.
All three branches and both parties are in rough cahoots. They all believe in a strong(er) federal government.
The elected branch (Congress) wants to avoid accountability, and pretty much does so. It can mouth complaints, but those words are designed to win elections, not to run a competent, restrained federal government.
I don't believe there is a solution. Universal suffrage pretty much guarantees the outcome.
That would, indeed, be a preferable situation.
But how do you propose to achieve such an admirable outcome?