Your mentioning four groups and noting three leaves an opening for another to be entered; namely the group that treats Ki development as an independent discipline to be studied in conjunction with Aikido waza. Tohei's break from Hombu was a major fracturing of the Aikido establishment and Ki Aikido has become a widely practiced branch of Aikido with offshoots of its own (Shuji Maruyama Sensei, Fumio Toyoda Sensei and Shizuo Imaizumi Sensei all came to America at the behest of Tohei and eventually founded their own organizations).
Saying four was a mistake on my part which I didn't catch... I never trained with any of these teachers other than Imaizumi Sensei but I would put him squarely in the third group which sees a unity between the physical practice and the spiritual side. Based on what we saw at the Expos and at Rocky Mountain Summer camp when he was a guest instructor, he is very much a picture of early Tohei; as he was just before the break up. His is exactly what I consider to me a balanced practice with a deep spiritual connection coming directly from the practice, solid technique, highly developed sensitivity and solid weapons training. I consider him to be one of the greats... I will be in New York teaching in March and I am hoping to have dinner with him while I am there.
I don't see these teachers as a fourth way although I have certainly encountered a number of Ki Society people who would definitely fall into my 2nd group. Lots of ki exercises etc and no ability to apply the principals at all. This was not true of the early teachers. So once again we have an issue of the transmission being broken...