I'm sorry Mike - I must be too dense to get the description. Apologies.
Let me try and participate with what I'm thinking anyways - please/thanks.
I want to say that this question is interesting and thus that I would like to participate in the discussion. Yet, at the same time, before I do, I would also like to say that while I am sure we may learn a lot by reflecting upon these things, we may in the end be making a bit too much out of nomenclature here. That is to say, the names of the techniques are fairly new and so the delineations between what is actually being prescribed may simply be reified (unnecessarily) through our opinions. That said, I am understanding the question to be: What makes a Kokyu Nage a "Kokyu Nage"?
I as well draw a distinction between "kokyu-ryoku" and "Kokyu Nage." All waza should utilize kokyu-ryoku. All waza should utilize kokyu-ryoku to the same level (i.e. as much as possible). Thus, I do not delineate a "Kokyu Nage" but the presence of "kokyu-ryoku. Nor (inversely) do I delineate "Ikkyo" by the absence of "kokyu-ryoku." Both include "kokyu-ryoku -- as should striking, kicking, choking, cutting, stabbing, but also standing and sitting as well, etc.
Aside from noting "Kokyu Nage" as a generic term that covers waza not in possession of their own nomenclature, for me, a "Kokyu Nage" is also a throw that tends to affect the geometry of Uke's body by the physics of the encounter alone (or for the most part). For me this stands in contrast to waza that either divide the tasks of affecting Uke's body by both a given tactical geometry AND a utilization of the physics present, or from those waza that are dominated more by a tactical geometry (with the physics involved playing a lesser or zero role altogether). In short, what one is noting the presence of a higher acceptance of energy prints as they are and a lesser presence of manipulating energy prints. Thus, for me, a trait of "Kokyu Nage" is that it is marked more by what can be called "Target Availability" and less by what can be called "Target Creation." Therefore, one can see that (for me) a "Kokyu Nage" is not about how I present myself (i.e. with kokyu-ryoku) but rather about how I allow a certain tactical scenario to present itself to me. In the end, for me, the highest ideal is to make every throw a Kokyu Nage.
To (maybe) help what I am trying to get at here -- please look at the following video;
For me, the first throw is a "Kokyu Nage" and the other throws could be called "Kaiten Nage." In the first throw, Uke's tactical geometry is ultimately deconstructed by the physics involved (more so than by a direct geometrical manipulation). In the following throws, Uke's tactical geometry is deconstructed by the direct attempts to execute "kaiten" (e.g. Uke's arm is always taken back and up over the top apex of the circle in combination with whatever else is going on).