THE SOLUTION IS SIMPLE<p>I suspect that the reason curling stones curl the way that they do is primarily due to one side of the stone being subjected to “static” friction while the other side experiences “kinetic” friction. This would also explain why the curling doesn’t start to happen until the stone’s linear velocity has sufficiently decreased.<p>If a stone is moving down the ice, away from the observer, and spinning to the left (that is, counter-clockwise when looking down on it), the right-side edge of the stone is moving in the same direction that the stone travels while the left-side edge of the stone is moving in the OPPOSITE direction that the stone travels. This means that the right edge of the stone is moving faster across the ice than the stone’s linear velocity. And the left edge of the stone is moving slower across the ice than the stone’s linear velocity.<p>As the stone’s linear velocity decreases, there will come a point when the left edge of the stone is no longer moving relative to the ice, while the right edge of the stone is still moving at 2 times the stone’s linear velocity relative to the ice. This means the left side of the stone is now being subjected to static friction while the right side is only being subjected to kinetic friction. The force opposing the left side of the stone is greater than the force opposing the right side of the stone, causing the stone to pivot around the left edge of the stone, “curling” to the left, until the stone's linear velocity reaches zero.