Re: Irimi Nage as Kokyu nage?
Several years back now, I remember just thinking of kokyu nage as a catchall phrase - mainly for when sensei didn't have a good name for a throw they liked, and that iriminage was just a specific version of kokyunage (being a super set). That kind of helped me organize things well enough in my mind at the time. It's not a terrible way to think about it today.
Here are some other odd things about iriminage:
Physically what I do for tenchi nage (ura version) is pretty much what I do for iriminage with the main difference being that uke is facing me for tenchi nage, and uke is not facing me for iriminage.
I can also do all 4 letters of the Y M C A song while doing iriminage if uke attacks with their right arm. (If they attack with their left, the C would be backwards).
Other wierd things are that my hips and arms are rarely moving the same direction at the same time - it's like a big moving rowing exercise done in 180 degree rotations.