I respect naka tatsuya sensei, but I don't think 80 - 20 and 20 - 80 hand power distribution affect your stance. as long as it is kokutsu dachi, it will be 30 front leg and 70 back leg once you stop your hand movement.
Naka Sensei is not talking about weight distribution nor distribution of "hand power" per se. That is just memory tool to understand where to focus INTENTION. According to him, even in back stance where (as you point out) weight is mostly on back leg, still the combative intent is forward (hence he emphasizes to focus on the front gedan barai of the double block manji uke) Ultimately he is teaching about internal budo and best connection of body structure to hara and the ground. He talks a lot about that and in his videos has many more exercises and examples of this.
It can be clearly seen here that the techniques come exclusively from the extremities. Oh well! The entire body structure is not active. The result should actually be known to all serious karateka.
Wrong.The Heian Godan is diferent. If you want to know the right way, check out the Shito kai Heian Godan kata. You, Shoto Kan, may God forgive you for your many mistakes.