I could see Criterion making it happen. They did lavish editions of Armageddon and The Rock, films released through Disney’s other studio divisions.
There was also a Criterion of Kagemusha, a movie released by Fox.
I don’t see the Criterion scenario ever happening, though. We’ve been dreaming about that ever since the GOUT and it just seem unrealistic that one of the most popular movie franchises ever wouldn’t be handled directly by its copyright holder.