Hi professor, thank you for following up on this! Sorry I forgot to reply to this. So it is still a bit of an interesting unresolved issue why there would have been any confusion of "Yamato" and "Daito" in the spoken language when referring to the name of Takeda's art.
Many thanks for the response. Are you familiar with Takeda Tokimune's account of the origin of the art, including the name? The account appears on p. 42 of Stanley Pranin's Daito-ryu Aikijujutsu
interviews. The Japanese text appears on p. 272-273 of Mr Pranin's 『武田惣角と大東流合気柔術』. Tokimune states that Daitou 大東 is the name of a place in Oshu 奥州, northeastern Japan, where Shinra Saburo Minamoto no Yoshimitsu stayed when he studied human anatomy. Saburo was a descendant of the Emperor Seiwa (850-881) and dissected corpses. He called himself Daito no Saburo 大東の三郎. Katsuyuki Kondo also mentions Shinra Saburo in his interview (Pranin, p. 154; pp. 133-134 of his Japanese edition.)
The problem is that Tokimune had a similar position in respect of Takeda Sokaku as Kisshomaru Ueshiba had in respect of Ueshiba Morihei. The difference is that Tokimune places Sokaku (and himself) firmly in a line beginning with the Emperor Seiwa, whereas Kisshomaru places great emphasis on Ueshiba as the start of a new line. In both cases, there is, shall we say, a certain looseness in the treatment of the historical evidence.