The truth is probably that Onisaburo Deguchi came up with the word, and was thinking specifically of spiritual practices. He got Ueshiba and Takeda to adopt the word to their art. The both ran with the word, and so did their students, and we have a dozen, slightly different, legitimate definitions of the word "Aiki".
This discussion happened years ago, didn't it? Pre-Ueshiba use of the word "Aiki" is pretty well documented. Check out the cover of "Budo Hiketsu: Aiki no Jutsu", from 1900, on this page