It’s interesting that you mention the Russian hymns, David. Here in W.Va., out Wayne county, there is a Russian Orthodox Monastery near a well-traveled lake. A buddy and I were at the lake one day, fishing, and as we were driving out of the holler that leads into the area, we noticed a sign for the Hermitage. We decided to check it out, so we drove up the holler that leads to their campus. They were actually outside, for some sort of procession, all dressed in black robes chanting what I assume is ancient Russian hymns. The flow of their voices did in fact remind me somewhat of the shape note singing I was familiar with. It was interesting to watch the monks, and they were very welcoming, inviting us to eat lunch with them. When one thinks of Appalachia, Russian Orthodox monks do not usually come to mind — but here they were, singing in an ancient language I did not understand.
Shape note singing is somewhat common here, especially in very rural areas (though, even it is dying with declining populations). So I have had many opportunities to experience the “stopping power” that you speak of. I wish everyone had the opportunity to hear it, if even once. It’s the tiny experiences like this that make my life so rich.