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).
I watched the Tohei initial film on Shin Shin Toitsu Aikido on YouTube recently. I hadn't seen it for many, many years and at the time I first saw it, I didn't really understand what he was showing. Now I understand it and, to be honest, I sort of admire his approach to things (although I don't think he was as explicative as he could have been, but that's simply a personal viewpoint).
The idea that "Ki development is an independent discipline" is actually the gist of the argument by not only Tohei, but by Akuzawa, Dan Harden, Inaba Sensei, Abe Sensei, Ushiro Sensei, and many, many others, if you think about it. It's not unique to Tohei... Tohei simply tried to codify an approach and make it an overtly visible part of Aikido training (at first. Later he went off on his own thing).
I like Tohei's approach, particularly as I saw it in that film (it's on YouTube in 5 parts; easy to find if you enter "Koichi Tohei"). The film approach is more coherent than the eclectically-mixed stuff you see at so many Ki-Aikido dojos. In fact, the way that Tohei explains the combination of Ki-training and Aikido is pretty darned logical, on that film. If you understand what he's talking about, of course. The way to add Ki back into a lot of Aikido is actually going to have to be done very similarly to the way Tohei laid it out... it's just going to have to be a lot more clearly explained, in terms of the basics.
My 2 cents.