Origin of kata-guruma?

Question

In an interview with Torahei Ochiai in the 1920's, Jigoro Kano states that he adopted kata-guruma from wrestling's fireman's carry.¹ However, the Kodokan Judo Throwing Techniques book posits a different origin, an adaptation of a koryu jujutsu throw (ostensibly via Kyutaro Kanda).^{2 3}

Do we know which of these is the true origin of the throw as practised in judo?

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Sources

1. I recall another anecdote from my days at the Fukuda dojo. Normally, I did not have a particularly hard time when practicing with Aoki and the other trainees. In the case of Fukushima, however, it was a completely different story. I could not overcome the strength nor disturb the balance of Kanekichi Fukushima no matter how hard or how often I tried. Finally, I resolved that I would learn to throw him somehow or other. After giving the matter a great deal of thought, I decided that a sumo technique might be effective against him. Upon hearing that a former sumo man, Kisoemon Uchiyama, worked at my university dormitory, I requested him to teach me sumo techniques. The sumo throws that I learned from him, however, proved to be totally ineffective against Fukushima. It then occurred to me to research books on western style wrestling, so I went to my local public library in Yushima, Bunkyo Ward. Unfortunately from among the wrestling books available, there did not seem to be any throw that I could use on Fukushima, except one that I thought just might be effective against him since Fukushima was taller than I. This throw was a shoulder wheel or kata-guruma. I experimented with it on one of my student friends soon after reading about it and succeeded in throwing him. I also tried it on Aoki with the same result. On my next visit to the dojo, therefore, I challenged Fukushima to a practice, and for the first time in my life I successfully threw him with my newly acquired technique. After many months of trying, I had finally managed to down him. I was overjoyed and felt a great sense of achievement.

   • Judo Memoirs of Jigoro Kano

2. There appears to have been a prototype of kata-guruma in koryu jujutsu. Kyutaro Kanda, 9th dan, is widely known as the master of kata-guruma and is thought to have developed the original kata-guruma from kinu-katsugi of the Yoshin-ryu Totsuka school. There is also a similar technique in Yoshin-ryu, called hankai-garami. However it is unclear if it has any relation to kata-guruma. There exists a further technique in sumo wrestling known as sori-te (Sumo wa koshite miru no ga tanoshii, published by Baseball Magazine Co., 1992).

   • Kodokan Judo Throwing Techniques (p.36-37)

3. That the throw was introduced to judo via Kanda seems obviously false given kata-guruma was part of the original gokyo-no-waza, standardised in 1895, two years before Kanda's birth.