Re: Sword tip movement
I hope we can hear all kinds of advice-- although the question is simple I think it may be related to some really interesting, fundamental aspects of movement, so thanks for the question.
For my response-- I currently use the suburi not to practice cutting someone with a sword, but to help fix (unify or purify) my body. Sounds like maybe you feel similarly. So, from that point of view, I'm not thinking much about sword tactics (I'd have to find a sword teacher for that). So I don't worry too much about the cut's trajectory and things like that. But I do agree that when your suburi is wiggling in its motion, in ways that you didn't intend, then it must be a sign of something wrong.
The way I see it, our bodies are capable of complicated motions, but you are practicing making a very simple one. Those wiggles are like higher harmonics in a sound, when you are trying to generate a pure-tone. I think the answer has to do with relaxing away unnecessary tension throughout your body, and not doing movements that you don't need to do (it might not be in the arms, could be legs or hips or back). One way a smooth suburi can happen is if you just let it result from simple movements of your center, as opposed to thinking about "doing" the cutting.
I don't know, that might all sound like BS, let me know if you think so, maybe I could clarify what I mean.