My apologies, as of instructor I am failing to make my point. The system is structured. Sure you've heard the statement sometimes you find the answer before, during, or after. What this refers to is the components that make up the art. Let me try this the Venetian blind theory. A short step almost squared to your opponent, could be considered short range or the first part of the Venetian blind theory closed. Using a one hand push you would have triggered salute push to your left shoulder. If you learned snapping twig, center of chest push which is taught as a left hand push. And as you yourself said most people are right-hand dominant while attacking so learn snapping twig for a right hand push which ends up center of chest because of the deeper step, or part two of the Venetian blind theory. Now glancing salute taught as a right hand cross push is even a deeper step or part three of the Venetian blind. The deeper the step the further your stepping foot moves to your left changing the point of contact further to the right of your opponents chest. Now you learned triggered salute first, which is the first part of this grouping. But you learned glancing salute second, which is the third part of this group, then you learned snapping twig on the left which really is the second part of this grouping. So the depth was not taught in order. And if you don't learn snapping twig on the other side you've left out a right push to the center of your chest, which would throw a monkey wrench in what you are saying about right-hand attacks being more important than left hand attacks.
Pushes are structured the same way. Short step, delayed sword, grab push, second Venetian blind, little deeper step, but learned as a left grab to center of chest, Lone kimono, grab with push. Conquering shield also learned as a left hand center grab pulling. And so on and so forth. And again if you use the right-hand dominant way of thought, you need to learn these left hand grabs on the right. But he systematically worked grabs all the way around the body pushing or pulling.
Mr. Parker has a great section in the higher manuals about learning how to think. In encyclopedia Kenpo under first cousin/second cousin moves gives an example of the Venetian blind theory, he doesn't say Venetian blind theory but it's what it is. " For example the techniques attacking Mace, flashing wings, and circling the storm all have the same father/mother movement, as well as the same brother counterattack. They may then be used as one single idea that may be varied as the situation dictates". If you notice in yellow belt in the Parker manuals short form one the punches are to the chest. Attacking Mace is to the chest. Part two of the Venetian blind theory. Flashing Mace is to the chest, part one of the Venetian blind theory. Now removing the club from the hand of your opponent for the thrust to your chest is part three of the Venetian blind theory. The punching hand on all three of these techniques originate from the opponents chest or horizontal punches. Mr. Parker was a master of hiding the system while explaining the system. The Dragon.
He actually said once, he would hand a black belt to the person that figured out how he constructed the system. When a person truly understands the system, such as path of travel, angle of execution etc. the student should be able to respond to each technique without being told which technique to use while testing.
If you understand, path of travel of your storm techniques, capturing the storm, 6 to 12, left to right. Securing the storm 9 to 3. Calming the storm 7:30 to 1:30 left hand block. Five swords 7:30 to 1:30 right-hand block. Read five swords in book 5, it doesn't reflect the photographs that are laid out beside. In all of these techniques work with allowances such as five swords works from 9:00 to 7:30 as Mr. Parker calls adjusting your angle of arc. By understanding these path of travel the student knows which technique to use without the instructor telling him, kind of important on the street. This applies to all techniques.
Hope this might help.