Even in the 1935 Asahi Film he seems to use kokyu nage the majority of the time.
I agree, and that film even has a section explicitly entitled "Kokyu nage," so it's not the case that we are interpretting his movements wrong.
Kobayashi sensei also reiterates here,
saying that kokyu nage was discouraged before the mid 1950s: "techniques like Kokyu-nage were only done after we started giving demonstrations," in the section about training after 1955. "So, if you did those techniques in front of Ueshiba O-Sensei you would be scolded. He'd say things like - it's just impossible to throw anybody that way."
I think it's certainly likely that since Kobayashi sensei started in 1954, maybe what he says is true regarding a subset of the timeline of aikido. Which might mean that in 1935, kokyu nage did exist, but only in a way that didn't "stick" permanently in the training regimen. (Maybe even then it was not something that O-sensei had the students do.)
I think the quotes are interesting. My current interpretation is that O-sensei was perfectly confident in what he
was doing, but saw what his students were doing as something different altogether: "it's just impossible to throw anybody that way." (i.e. "what I was doing to throw people is not that.")