Do some people shuckle when they daven because they have a hard time standing still without moving and shuckle to help ease this unpleasant feeling of being forced to stand still?
Maybe for some, but I think for most people it’s social/cultural. That’s why when you look at a crowd devening most people are shuckling, even though most of them don’t have ADHD.
Rav Soloveichik is quoted in “On Repentance” as saying that when he told the chazan in his shul not to repeat words he was told that that would ruin the tune. Apparently some people do not know the difference between a bet knesset and a bet opera.
I have heard some significance on shuckling during daveinng. when your leaning forward while davening it symbolizing ahava for Hashem, and leaning back is for yirah. I find it very effective in kavanah also.