Yes, absolutely, agreed on the tightness emphasized not only by heavier weights but also by the cleans. The laziness lighter bells encourage, or allow, is one of the reasons I love moving up. That feeling of wrangling a weight that requires total body tension is what I love about weightlifting. And I too think cleans are the best exercise for working on the upper-body side of that ballistic equation. You feel you're doing well when you hit that cement wall at the end of the movement and everything feels locked in place. For sure it will give you a better platform for pressing.
Regarding the push-press, it matches what I have been thinking about these movements outside the more traditional ones (swing, snatch, press, squat - "traditional" in the sense they're more central to most programs) as ways to circumvent the difficulties the kettlebell presents as an implement. In the same spirit of including heavy cleans as a way to do ballistics with heavier weights, shouldn't we (well, I) be push-pressing heavier weights together with the presses, as a way to progress faster? And bent-pressing even heavier, for that matter?
The "unloadability" of the kettlebell is the biggest problem when it comes to progressing. If your 5RM press is the 32kg and you can't press the 36kg, then normally what you'd do is press the 32kg until you can do it with the 36kg. I want to program in a way that gets me moving heavier weights with these other movements.
It requires having many bells, which I don't like. The strongest point of KBs to me is how easy they are to store and how much you can get out of one (or one pair). But when you start wanting to go heavy, and work with doubles (my goal is 2x40kg, at least for presses and squats), you notice how this is dissipated. Everytime I want to go up, say from 24kg to 28kg, I have to buy a new bell, which means paying for the 24kg of iron I already own, and then for the 4kg I wanted. And because you can't stack bells on a pin or on top of each other, like you would with plates, they end up taking up a lot of space.
To summarize: I'm thinking about a program where you clean, swing and snatch with different weights, and bent-press, push-press (maybe jerk) and double-press with different weights, and maybe also split-squat, double front squat and goblet squat with different weights, but wonder if I'm not flying in the face of the implement's nature.