This all falls on Trump. He when he heard Sessions recused himself, he should have Fired him that second, we would have been saved from this Insanity., and he has had other chances to Fire Sessions and Wussed out. Trump can fire Sessions and appoint Pruitt ( WITHOUT CONFORMATION) but I doubt he is even aware of that.
That route - the Vacancies Reform Act route you refer to - would trigger a legal challenge as the language of the VRA does not say that a President can replace a FIRED confirmable officeholder, merely one who “dies, resigns, or is otherwise unable to perform the functions and duties of the office.”
There are arguments both ways, but it’s not hard to imagine an uber-liberal appeals court like the DC Circuit staying the appointment of a DOJ through the VRA method, which would presumably leave Rosenstein in charge.