I have always wondered about the theology connection. Tomiki, apparently studied all the Omoto-kyo texts in an attempt to understand Ueshiba's Aikido - he certainly thought the connection was important. Relatively few of Ueshiba's students delved to that depth and even today his honbu dojo has an Omoto-kyo shine (regularly blessed). That does not mean Tomiki accepted the Omoto-kyo teachings or that there wasn't a particular connection with Ueshiba's views on competition and his religious leanings but it does make me wonder about your premise.
I have become more convinced that Omoto is a crucial factor in understanding Ueshiba's martial thinking. What is available in English is OK as far as it goes. Kenji Tomiki had the advantage of living in the same era and of being able to talk to people like O Deguchi directly. However, I know that K Chiba, for example, did not accept Morihei Ueshiba's theology and at least one of my older aikido friends did not do so either. He and his family embraced Buddhism and he had no reason to change to Omoto merely because he was a student of M Ueshiba. R Shirata entered the Kobukan Dojo because he was already in Omoto, via his family. As I stated elsewhere, postwar Japanese deshi who entered the Aikikai Hombu will not have studied Omoto because of its connections with ultranationalism, and such study would have been discouraged after the war.