Would have had to have been

But belying the quiet that settled over Roswell, a thousand miles away, part of the U.S. military went on wartime alert as bits and pieces of the craft reached their destinations. One of those destinations, Lt. Gen. Nathan Twining’s desk at Wright Field, was the focal point from which the Roswell artifacts would reach the Foreign Technology desk at the Pentagon.
Among the first of the army’s top commands notified of the events unfolding in Roswell in early July would have had to have been Lieutenant General Twining’s Air Materiel Command at Wright Field, where the Roswell debris was shipped. Nathan Twining has become important to UFO researchers because of his association with a number of highly secret meetings at the Eisenhower White House having to do with the national security issues posed by the discovery of UFOs and his relationship to National Security Special Assistant Robert Cutler, who was the liaison between the NSC and President Eisenhower when I was on the NSC staff in the 1950s.

The Day After Roswell

Hi. Why is "have done" used twice in the construction in this context? How should I make sense of the red part?

I think "would have done" indicates a speculation about past and the "have been" part indicates the top command (i.e. Lieutenant General Twining’s Air Materiel Command at Wright Field) was already there before the Roswell debris was shipped there.

Does my analysis make sense?

Thank you.