Indeed, how much import is given to the connection with Omoto religion? Not enough in my view. The connection with Omoto and Deguchi was all important I would say. Inoue was quite open about this.
Most likely everyone is familiar with it, but I would like to recommend Frederick Franck's book " an encounter with Oomoto, the great origin, a faith rooted in the ancient mysticism and the traditional arts of Japan (1975).
Franck witnessed a demonstration of Inoue's Shinwa Taido and describes it as " a particular esthetic form of Aikido".
He explains how the "sensuous life-affirmation of animistic Shinto fused with Buddhist acetisme and eschatology and Confucian precepts as filial piety and human-heartedness" was inherited by the Oomoto kyo. "In this spiritual and moral climate the Sacred is not verbalized or systematized, but experienced in manner one might characterize as esthetic". The Oomoto kyo see according to Franck, the esthetic experience in the traditional Japanese arts as poetry, painting, calligraphy, silence, humor, dance, theater, Aikido, as a way to experience the Sacred and to transmit religious moods and values.
The Oomoto kyo see Aikido as a spiritual practice / experience. Not as a fighting method.
Frederick Franck makes an interesting comparison with the French philosopher Teilhard de Chardin and the words of Nao Deguchi and Onisaburo Deguchi. Reading the spiritual ideas of the founders of Oomoto kyo everyone can see where many of O Sensei spiritual thoughts must have had its origin.
It is a small book, but it is filled with nice details and interesting facts.
Frederick Franck (Dutch - American) is known for books like "The Zen of seeing", his art work, and the work he did with Albert Schweitzer. He is the designer/sculptor of the chapel of peace at his home in Warwick, N.Y.
All the best!