What would it mean to move the Dept. of Justice out of the Executive Branch?

Just a hypothetical: What would the implications be of moving DoJ out of the umbrella of the Executive Branch for the purposes of avoiding conflicts of interest?
Say, something along one of these lines:

  1. Make the Attorney General an elected office (it is in some states, isn’t it?,) not appointed by the President. People in DoJ who would now have been appointed by the President and approved by the Senate, are now appointed by the Attorney General and approved by the Senate. AG and others may be removed by impeachment, just like judges.
  2. Make the Attorney General and the heads of units within DoJ quasi-independent like the Federal Reserve. Congress sets the agenda as impartial law enforcement, President appoints the Attorney General and heads of units within DoJ with Senate approval to 14 year terms, and these heads serve with the AG on administrative committees with rotating voting powers, much like the governors of the Federal Reserve Banks. AG and others may be removed by impeachment, just like judges.
    Neither plan would entirely remove partisan political influence - that’s impossible. But they might mediate the more immediate and blatant types of influence.
    Clearly the Constitutional amendment necessary to create either of these scenarios is impossible save the invention of the orbital mind-control lasers. Don’t fret too much about the current implications, just the structural ones - pretend it happens in 2028.
    Are either of these schemes unworkable for some reason? Obvious or non-obvious flaws are welcome.

nm