I find your answer most interesting yet, especially about Article II.
Apparently the president can appoint temporary advisors that does not need approval from congress. If Mr Musk qualifies for such appointment I guess is that something for the courts to decide. I guess that implies that the audit itself is time framed.
In the Appointments Clause case challenging Musk’s role, the Administration has said Musk is officially an non-decision-making adviser (not a temporary one, just a generic White House staffer not requiring confirmation), and completely unconnected from US DOGE Service.
Oddly, they failed at the time, on direct questioning by the judge, to identify who the Administrator of US DOGE Service currently is.