Re: Shodokan, Tomiki, Aikikai?
I'll address a couple of your questions. Shodokan is the name of the style. Tomiki is the name of the originator of the style. The use of "Tomiki Aikido" is a euphemism to describe the style originated by Tomiki.
Also, Jigaro Kano did not study with O'Sensei, but was impressed by him. Kenji Tomiki was one of the high-ranking Kano students who was dispatched by him to study with O'Sensei, in order to bring a better sense of what he was doing back to judo.