Then what is the way to do it?
I would agree that, since aikido is ideally both a search for and an expression of something greater and more important than just a martial art, trying to define it technically seems on the surface to be a bit narrow. I would also agree that Ueshiba himself never defined aikido so narrowly.
But for the purposes of language, both those things are secondary concerns. Our primary concerns are (a) having a word that can function as the name for our martial art, and (b) keeping the definition of that word specific enough that it can be used functionally.
If we are not going to define aikido according to technique and lineage, then how are we going to define it?
I think you have kinda answered your question. For me, I am working on defining my aikido by functionaling expressing... aiki. Aiki is the "something greater than" component of our curriculum. Bill Gleason said in an interview that he felt most aikido people were not practicing aiki. While controversial at the time, we now hear this from other people and we now have other people than can demonstrate Gleason Sensei's point.