As for Funakoshi, I have no doubt that he was at least aware of Karatedo Taikan and the meeting of the Karate-do Promotion Association. This is not surprising as Nakasone was working as a publisher in Tokyo from the early 1920’s onward and quite naturally being the political and social center of Japan, the book was printed and published there first. If you exam the remainder of the tweleve introductory kata in Karatedo Taikan, you can see that it introduces age-uke, mae-geri and a few other basic techniques. With some very minor modifications, you can see where the Shotokan Taikyouku kata may have come from.
Going back a little in time, we can find the first inter-style association being formed with the Toudi Research Club. It made it all the way to an independent, privately funded, self-contained facility by 1925 with Miyagi, Motobu (Choyo), Mabuni and others acting as the main instructors. Not to mention a whole host of guest instructors who would drop by: Yabu, Hanashiro, Kyoda, Go Kenki, To Daiki, etc., but t the Kenkyu Kai ultimately failed by 1930.
I mention this, because at this time, the Toudi Research Club did not appear to have used Fukyu kata, but instead concentrated on the ko-ryu kihon kata (San Chin and Naihanchi). Students simply trained with whom-ever they pleased or whoever was teaching at the time. Fast forward in time to the mid-thirties and you have Miyagi visiting Shanghai and training briefly at the Jing-wu; an organized, government funded institution with a standardized curriculum and fundamental kata which cut across styles. Not long after we find Miyagi involved in the Karate Promotion Society and presto, we have twelve new Fukyu (promotional kata). Of course it may simply be a coincidence.
For reasons I have yet to understand or fully explore, these kata were never adopted by any karate organization. Not one. They were completely abandoned and we have yet another set of kata being developed by Miyagi and Nagamine in the 1940’s. And 50 years later the Okinawa Board of Education petitioned local karate instructors to develop other introductory kata as recently as the 1990’s. To what end, I do not understand, but several were developed.