KKW came from the Korea Taekwondo Association. The first president of the Korea Taekwondo Association was General Choi, before he left to start the ITF. It would seem that his influence would be in your lineage, with Un Yong Kim between you and him.
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Korea Taekwondo Association - Wikipedia)
Funakoshi taught Choi and a few others who brought the art to Korea and modified it. Who exactly is the creator, from whom you want to learn this stuff? These moves have not been new for a long time... they are much older than Funakoshi and his teachers even. If you want to know what the original creators wanted you to learn... that line would take you through Funakoshi and Choi and the other Koreans who trained under Funakoshi, before creating TKD. If your creator is someone more recent... then your creator's lineage and where he learned things also would come through that same line. But, you don't want to look at any of them, and still want to know what the creator wanted you to learn... Ok. You will have to be specific about who you consider the creator to be.
I am not surprised at all that you don't train the same way as Karate. I am surprised that you claim to train differently than any other TKD school or practitioner I have ever trained with or talked with. (its been quite a few... I spent 3-4 years training in a TKD dojang... but would frequently train with the TKD class as well... The TKD master and I were pretty good friends and would cross train with each other quite a bit... and talk about what we were learning and how... additionally I have been on both sides of the US training with TKD guys in various fashions, and have a great deal of respect for TKD)
In this case you are reading into things, what isn't there. The only guidance I ever wanted to give you was to look to the founders of your system, and see what they wanted to teach you in your forms. Apparently, I have not been able to decipher who the "creator" was. But, once I find out, the only guidance I would try to give, is to find out what he thought that answers were and maybe look to where he learned from. And then explore from there. Many of the things I have shared are things that I have learned from TKD people (masters and students) that helped me start looking for the same answers you are looking for.