The gentle movements to distract the bird that you are describing work well with some birds. I also agree that providing toys and treats for their beaks to work on is great, too. Imitating the sounds they make to one another when the others bite them too hard is also helpful. All of your posts have been very good.
Birds are individuals, and the secret is finding what works for each bird that the owner is also comfortable with. I use the gentle hand movement with both the green cheek and the parrotlet because that distracts them from biting without frightening them in the least. Green cheeks in general are very skilled at hanging on. My green cheek never falls off of my shoulder. The parrotlet is not as good at hanging on as the green cheek, so I have to be very careful I don't dislodge him. That having been said, those two have very similar personalities, so I am not surprised that similar communication methods work equally well with them.
The linnie has never bitten hard enough to hurt in the least, so I would never have had to show her she was being too hard. The grey only bit me too hard once several months ago while she was still being hand fed. Nevertheless, I have to say that I do not plan to ever use any type of quaking movement with either of these birds. (I can't say what my unplanned reaction might be to an unexpected bite, but I would not "plan" to pull away or move quickly.) The reason I say this is because they are both very unsteady in perching on my hands. The linnie falls off a lot when I am just moving normally. She is flighted now, and I hope to keep her that way, so it is not a big issue, but I do not think it would ever make sense to move quickly with her because she would fall. The grey is not quite as easily dislodged as the linnie, but she comes pretty darn close. Additionally, the grey is so sensitive and easily frightened that I try to be very slow and deliberate with her. I think this method would be counterproductive with her.
To me, every method must be evaluated in light of the individual bird's reactions. Additionally, I do try to figure out if there isn't something rewarding I can do instead of punishing any time I am working to attempt to change any behavior. The bottom line with the green cheek, though, was that a slight hand movement never appeared to be "punishing" to her. She just seemed to realize it meant that she was being too rough. It would have been very punishing to the linnie, who would have been scared by it because she would have been taken off balance. It would have hurt our relationship instead of building it up. So, for her, I wouldn't have done it.