The more I've been doing with trying different hand positions the more I'm coming to think about hips. Here's what I think is going on. When I ride I naturally want to move some part of my body opposite to the force of my legs. Its just like running. When you stride forward with your left foot you reach forward with your right hand an bring your right shoulder slightly forward. Your shoulders rotate opposite your hips. If my arms are extended they tend to pump opposite my legs, and also help balance. This makes for awkward riding. When I hold my arms behind my back, my shoulders stay square and instead of arms and shoulders compensating for leg movement, the compensation focuses down at my hips and lower abs. I find that if I keep the hips and lower abs loose to work in collaboration with my legs, my shoulders and arms can stay quiet.
Now the first exercise I do when I get on the unicycle is to get the arms quiet, maybe even behind the back, and focus on getting the hips and lower abs loose, flexing, and collaboration with the legs. It makes for a more stable ride than with arms flapping. I think that may be because most of my fine balancing is being done by hips and abs very close to my center of gravity, rather than balancing by moving shoulders and arms which are more distant from the center of gravity, and where even small movements can add to jerkiness.
Here's a vid of the day's work.