Thanks for chiming in.
I will try and be brief -- as requested.
No, I do not have any nor do I know of any original sources whereby Osensei can be quoted as saying "This I am basing on Omoto-kyo" (or some other variant), etc. As for second hand sources, there are only those various figures inside and outside of Aikido that mention the influence that Omoto-kyo theology had on Osensei. However, there is no other secondhand source that I know of that has someone saying "Osensei told me that he got this from Omoto-kyo." All of them only talk about the influence the theology had on him -- as they witnessed it secondhand.
In short, as I said above, and in the essay, this is the hypothesis of the whole piece: That Osensei's thought has been heavily influenced by Omoto-kyo theology. As a hypothesis it is not something I would expect to be provable in any kind of direct way. I am coming from the view of cultural influence. I understand this in the same way, for example, that we know that Chinese culture influenced Japanese culture -- though we have never found a text written by anyone from Japanese culture to read explicitly, "I have been influenced by Chinese culture."
Your second question is one I would see as requiring a very long response, one I am not sure I am even yet able to write. I am sorry. Let me say this though -- still trying to be brief. The question as I understand it can be taken in three ways: a) How does Omoto-kyo suggest we apply ichirei-shikon in our lives (since they may not at all be talking about Aikido); b) How does Osensei suggest we apply ichirei-shikon in our lives (since he most likely will talk about Aikido); and c) How can we apply ichirei-shikon in our lives. For the first two takes on this question, more historical analysis will have to be done. For the last take on the question, I would say the answer is a very personal thing -- one that takes full advantage of Omoto-kyo's position on the universality of Man's inner nature and God, etc., and thus of the applicability of all creeds, practices, and doctrines. What one requires then is not so much a specific creed, or a specific practice, or a specific doctrine. What one requires is a specific quality -- one which may mark our creeds, or practices, and/or our doctrines, etc. In particular, one is looking for ways to generate, for example, the five drives or capacities that mark the spiritual life through one's training. A possible example of this, though not brief, would be the way that a sense of shame is being used in one's practice as it is being discussed in the above mentioned thread -- pasted here below as well.
Another possible way is to see what is being cultivated as it is being mentioned here:
And, there is also this thread:
Finally, from our own web site, there are our Budo Contemplations and our Exchanges -- which also mention such things. (The Exchanges are much more brief in their discussion.)
Outside of this, I am afraid I have not formulated for mass consumption (i.e. in brief form) my own practice nor my own pedagogical slant concerning such things as they are played out in our dojo. I hope that one day I will be able to do so.
I too look forward to meeting one day -- it would be a great thing to discuss many of these issues, and other issues as well, with you. Please always consider yourself welcome at our dojo. This next year, I am planning to attend the Expo -- so hopefully you will be going to the next one as well and I can meet your there.
Thank you very much,