"I found that I kept having to work more rope through knot-1 in order to be able to tie some knot-2 (maybe a jammed double-turn, just to give knot-1, the CHClove, its chance to shine)!"
You might find yourself in that position now only because you haven't worked with these constructs for very long.
Another thing about these constructs is that you don't have to keep tying and untying stacked component knots. Once the constructs that use stacked component knots are set, the constructs can be quickly and easily put into, and removed from, an application.
All of the problems have solutions, so no problems remain. Then, there are . . . imaginary problems, which turn out to be no problems at all.
Once you discover WHY the constructs (as I am presenting them) are valuable, you might find yourself liking them. My job is merely to introduce them to you--you know, to lead the horse to water.
"And I see that as a binding structure not a "binder" knot --its knot is a hitch."
Yes, the "Tension Binder" is the structure, and the Tension Binder's "Component Knot" is the knot, specifically a hitch, which is why I originally called the component knot the "Derived Hitch" and the "Component-Knot Hitch" the "Derived-Hitch Loop." Knot terminology is a mess because it has evolved over long periods with contributions from many, and because there are many nested structures and functions. I am probably wrong for wanting to attempt to influence an improving of it. So, since others will just call the knot and its constructs whatever they want anyway, I should probably just call it what I want. What's important is whether the contribution to the knot world has been made, because the whole point for the existence of the knot is its use by humans. Favorably, I am the only one who needs to know that the contribution has been made.
I will be calling the component knot the "Fixed Gripper." This is bound to incite an awful lot of comments like, "The Fixed Gripper? Why'd ya fix it? Was it broken?" and, from those who don't understand it, "The Fixed Gripper? If you ask me, you should call it the Broken Gripper, because I can't get it to grip at all." But, this situation will be useful.
JCS