My next point is more along the lines of Takeda developing his jujutsu "on the fly." I have always contended that this is why the major schools of DR are all so different. Why the Syllabus lack consistency. For that reason I considered and forwarded the idea that the art is fully based on aiki with no real jujutsu syllabus.
Bold is my addition. It's a point that I just reread and thought I'd focus on. I use Ueshiba as an example because he is a good proxy for Takeda. History on Takeda is not as common as history on Ueshiba.
There are quotes from Ueshiba, Kodo, etc that their art is formless. Aiki in the hands of someone who can use it freestyle validates that.
Even looking at Ueshiba and how he changed/altered/whatever the Daito ryu syllabus, it still fits very well that he built/used his spirituality upon his Daito ryu aiki. He used aiki in whatever he chose from the Daito ryu syllabus to enhance his spiritual-ness. Formless because of aiki.
It explains why Takeda would change the name of his art at the prodding of Deguchi. Aiki is central and formless.
It would explain why Ueshiba didn't have any problems with someone calling his art, Aikido. The way of aiki. At that point in time, he was working on that avatar of the kami-thing by way of aiki spirituality. I think the way of aiki to him was his way to the way of spiritual-ness.
As Dan noted, aiki being formless also explains the vast technical curriculum across the range of Daito ryu and aikido schools. Technique doesn't matter as long as the person is aiki.
Ueshiba is quoted as saying, "Aiki? I am aiki!" Takeda could teach whatever version of whatever jujutsu technique that he wanted, and could make it work because he used aiki. Timing (another famous quote by Ueshiba about aiki not needing timing) didn't matter so much, body placement didn't matter so much, because aiki created the openings, the timing, and the body placement. (See also Peter Goldsbury's article where he went over Ueshiba and ushiro training.)