Well, the key to all this seems to be Cyrus E Akers' story, and that is proving very difficult to pin down. A quick free trial at ancestry,com is helpful, to a point.
What it reveals is that Staff Sergeant Akers left the military in 1973. That's it!
What we can glean from his widow's records (she is still alive it would seem) is that she didn't seem to stray far from her home state of Michigan until moving to Florida with Cyrus in 1977. There's an interesting record of her returning to McGuire AFB from Germany with her son in 1959, but that's all we get - there's no record of Cyrus travelling with her. The passenger manifest lists the number of military personnel but they don't seem to need to complete entry cards. Her home address listed on the immigration card is a PO Box in Kinross township in Michigan. This township is not far from Rudyard, from whence the Akers' migrated to Florida in 1977. In 1960 she is listed as a book keeper for a company in Sault Sainte Marie, which again suggests she has left the military (both she and her husband were serving at the time of the Korean War). Gene's schools are both listed as in Michigan, and he attended College at Sault Sainte Marie, so it seems likely that he never went to New Mexico.
All of this suggests one of two things. Either Mrs Akers stayed with or near her parents in Michigan while Cyrus carried on working whichever base he was assigned to, or Cyrus was nowhere near Cannon AFB and served at a base in Michigan, such as Kincheloe AFB. He could equally have been serving in Vietnam, as listed on his gravestone. If he was at Cannon, he joined his wife in Michigan in 1974 before they left for warmer climes.
The idea that Cannon AFB was chosen for filming as a quiet and sleepy out of the way place is also nonsense. In May 1968 it was chosen as a training ground for the 4429th Combat Crew Training Squadron, and it was also a training ground for the many pilots being readied for service in Vietnam. It was pretty busy, and as such would have been a monumentally stupid place to pick as a covert filming location.
The idea that Armstrong and Aldrn wre also popping buy to oversee the proceedings is also pretty dumb, given that their training schedule was pretty intense even a year before their mission.
https://www.hq.nasa.gov/alsj/a11/A11CrewTrainingSummaries.pdfin summary: a dead guy says a dead guy said. The original dead guy said it, only then it turns out the other dead guy said it. The notes were stolen, and nothing else, but then a computer was stolen as well. The dead guy still manages to read the notes. All the other evidence was destroyed in a fire that hadn't happened yet. LBJ was there, while simultaneously partying with Hollywood stars and Apollo 11 crew were also there while at the same time training at the Cape. The secret location for all this was a busy training ground for soldiers and air crew.