Mathew, I think you've asked a very tricky question! Besides the wide inter-dojo variability within aikido styles, all the techniques you've mentioned (ex. ikkyo, nikkyo, sankyo, kotegaishi, koshinage, etc.) are also seen in Daito-ryu. When you have an 82% overlap in terms of physical techniques with another martial art, it seems like it would be difficult to "define" aikido according to physical overlap. I am definitely NOT saying that you are wrong, but I can see how others might see it differently. In my personal opinion, I think it comes down to a focus on developing "aiki" whatever the heck that is
The specific techniques and solo exercises are just tools to facilitate the expression of aiki. Thus, maybe it is possible to see high level karateka, judo and sumo players, and maybe even a dancer(?) expressing masterful levels of aiki.