What I'm asking is; what is that fundamental set of things that defines aikido for you?
I do not think it lies in the waza, so much as in the lineage. In terms of waza, what I am doing could just as easily be described as some form of Daito-ryu. But we know that what Ueshiba was doing received the name 'aikido' in 1942 and this is enough for me.
I must admit, though, that I have never spent much time looking for the fundamental things that would figure in a definition of what I am doing. I suppose that this is because (1) I have been trained in Greek philosophy and can see the problems involved in defining anything, and (2) all my teachers have had a very clear link with M Ueshiba and so it has not mattered very much.
Since what I am doing is a practice: a complex, habit-forming activity that does not have a specific objective other than the activity itself, the only way I can learn how to do it properly is by doing it and learning to do it better by imitating those who can do it better than I can. Sporting activities are similar, of course, and one of the reasons why I took up aikido is that it is not a sport. But this, of course, still leaves the field wide open.
My teachers have almost always been Aikikai, mainly because when I moved from place to place, the previous teacher recommended another one. But this was still rather arbitrary and if I had found a good Tomiki or Yoseikan teacher at some point, I would almost certainly have followed them.
So, to conclude, I have never searched for "that set of fundamental things that defines aikido" for me. Some people might have to do this and believe that they are not practising the art unless they have done this, but I have never had to do it.
This does not, of course, remove the need for study and I have found that periodically you have to go back to the beginning and recreate things, so to speak. Ecountering new teachers is a good occasion for this, since they invariably do things differently. A few weeks ago we had a joint session in my dojo with Nakao Shihan from Kobe. This was a good occasion for going back and looking again at how Seigo Yamaguchi used to practise.
I think there is a danger that by defining aikido too closely, too specifically, you will exclude much that is useful, even important.