My Father played a little with an index and router but replaced the router because of the tear out you mentioned. He used a small shaper head mounted to a big hand held inline grinder, the kind welders use to break edges, mounted to the end of a long bar. The bar had a universal joint from a car driveshaft that was fixed to a spot he wanted to get the right pivot point so it would arc across the work. He had templates he would position along the bar to create the curvature of the bowl etc. The blades in the shaper head cutting a large arc left a smooth surface needing very little if any sanding. I don't have any picture of the setup and the bowls are packed away for at least another 6 months or I would add them to the thread.
Pete