Hmm ok, i've never studied under Kanai senior students, but where I do they call it sumi/sumotoshi.. Maybe cause we don't speak Japanese and have bastardized everything.... But here's a clip of the same.
Sumi otoshi (corner drop) - one of the connections is at about the uke's elbow. Tai otoshi, one of the connections is at about the shoulder. Most otoshi are done with two hands while kokyu nage is mainly single-handed throw. My take.