The idea that Tohei's approach was a subset of the set strikes me as a rather self-serving position and one that would, to my mind, only be said by someone whose vested interest is in portraying it as less than what they do. I prefer to think of them as both having something to offer.
As I stated, the subset characterization is accepted by people in the place where Tohei focused significant effort to disseminate aikido outside of the U.S., and these people have first-hand experience with Tohei's method and Dan's method. Therefore, saying that this characterization would "only be said by someone whose vested interest is in portraying it as less than what they do" makes no sense: people here have been ardently trying to preserve what the founder and Tohei imparted first hand half a century ago. And, until three years ago, in Hawaii, frankly, only Chris Li was interested in what Dan and Mike had to offer.
Mike Haft wrote:
I do not believe anything Mike or Dan has to offer is something other than worthwhile and a good addition to most people's training. Nor am I deluded as to think I do everything they do, I do not. But having met and practised with a number of people who have practised with one or both of them, I'm very sure that what I do is broadly similar and totally compatible. Probably missing a few things but I'm in it for the journey more than the destination, so that's fine by me.
Everyone's practice is different. Good for you that you've tried to make rhyme and reason out of the general principles Tohei imparted. How has this work tied to what you've experienced from people who've trained with Dan and Mike, specific to spiraling / silk-reeling? This is the specific portion of the set that Tohei's subset does not address, unless it's some kind of okuden.
And, no worries if spiraling falls into the category of "being a good addition", and being one of those "missing" things. One of Dan's key admonitions is that practitioners focus on spiraling and other more complex movements -- over foundational connection and opening skills like one-point, keeping weight underside, and refining the ability to extend ki -- at their own peril.