... methods, how to take a balance of attacker in the moment of the contact.
Well, as far as I learned it, taking the balance is not an issue of timing or atemi or combine ones own movement with that of the attacker. But I learned that creating kuzushi is a matter of using what is called " atari" at us. And creating atari allmost seems to be a synonym of "making aiki".
In practice this means to have a contact somewhere between the bodies of tori and aite. Often it's hands or arms (relaxed, no grabbing, hands are open). But it is possible with every part of the body. This contact/atari effects the structure of aites body, takes his balance and make him collapse. (This is different from what some teacher do, creating contact from center to center. Even if the center/tanden is central also in this work.)
Learning to do this needs "special" excercises, not identical with the waza of aikido.
Aikido waza are one possible application of "making aiki", providing structures to use aiki in a certain way. But they themself don't teach aiki. They use it. This to me seems an important difference to other teachings of aikido a experience in some dojo.
This is - in very insufficient and a bit "helpless" words - what I learn. And I am still a beginner of this way of doing aikido.
... IP/IS extremists are not welcome here.
There is no IP/IS in the way it is meant and discussed here on aikiweb taught in our aikido. But the more you try to understand and to do it, the more you got to go and explore into yourself, your own body. What we do is clearly different from what is often discussed here. But it kind of points in the same direction: Getting aikido as a internal martial art. Which it often is not.