Re: "The goal is not to throw"
I honestly think people make this way too complicated and often way too "mystical" sounding when it really doesn't need to be.
As we learn something new we will tend to focus on details of a movement. As we start to focus on those details we tend to start to over utilize aspects of our bodies. So a nikyo where the students shoulder raise up and they start trying to power through it. Rather than keeping that connected feeling and simply moving through the entire body to cause the nikyo to happen. That connected body allows nage (or fill in your favorite term here) to "feel" what's going on in the other person's structure and applying the nikyo becomes rather simple (unless the other person is doing the same thing back with their own connected body and then you have a problem). So the idea of tensing, or "trying" to "make" it happen involve localized tension and a destruction of the smooth connections. Or as our late sensei used to say "when you try to throw you cut off the flow of ki. Let your ki flow." The interesting part for me is that after some years I now understand that much better (I think) in that now I can intend to throw without mucking it up. I just keep my focus on maintaining that relaxed structure which allows me to feel what's going on in the "aiki" of me and the attacker. It is both simultaneously very soft but potentially very powerful because, well, at that point I have them. And I can throw. Or not. So for me the focus is not so much not "trying" to throw, but more about getting that connection, getting the "feedback" started, and working within that to do what I want to do. Which might include a throw.