Josh - Fantastic information. If enough copies of the book sell to ever warrant a reprint, I will correct the information in the new edition.
Barring further info, I would still stand by my conclusion/speculation that this menkyo was symbolic, and demonstrative of a special relationship between Takeda and Ueshiba.
No, not merely "symbolic."
"Budo as love" and the Yagyu doctrine of katsujinken "life giving sword" are a close fit. Similarly, the "posture in kenjitsu" in the Yagyu katsujinken doctrine was founded on shuji shuriken, an esoteric concept described cryptically in the Heiho Kaden. Munenori's text describes shuji shuriken as joining "being" in the upward palm, and "non-being" in the downward palm in to one. This describes the the in/yo joining of the juji + figure.
There is also a Doka of O Sensei's with that very image of taking "in" in the left hand and "yo" in the right hand. This is tenchinage. While Daito-ryu has a version of this technique they call it aikinage -- the tenchi Heaven/Earth image of the technique name is only in aikido and is directly related to the juji + in/yo figure.
According the annotations, Yagyu Mitsuyoshi explained the secret doctrine of shuji shuriken as learning an enemy's mind from the cross-wise block, i.e -- juji +, That is very likely the "Cross of Aiki" as O Sensei wrote in several of the Doka that I already laid out above. Also as I discussed above, he referred to his art in a Doka as "jujido."
As to my presumption that he got mu-to training whether legitimately (assuming the menkyo debate is resolved), the emphasis of Yagyu on its mu-to system (whether he was certified in it or not) certainly had to inform their curriculum otherwise. Munenori says precisely that in Heiho Kaden Sho, that postures, sword positions, distance, movement, mental focus, feints and attacks were all premised on mu-to. "No-sword is central to all important things." Hiroaki Sato, tr.
I have previously noted these functional correspondences and specific references
, which we have discussed before relating to the Yagyu muto system
as it may have been adapted into parts of aikido. You did not -- then -- give me any credence for noting them
-- but perhaps you will revisit those points also when you have a chance..
Ueshiba claimed Shinkage-ryu as part of his influence
-- Aikido Journal still holds forth
that O Sensei was granted a Yagyu menkyo kaiden by Masakatsu Nakai in 1908 in Sakai City -- who reputedly was proficient in both Shingan and Shinkage.
Many sources attribute Ueshiba's menkyo kaiden to him and assert it was Shingan
Perhaps not -- or perhaps both.