Hello Rob, hope you do well. *"It seems one cannot move/snap the pivot on the model itself, which seems to be very counter intuitive..."* I'm on H14 and have a test Sphere. When i right click on the handle in Object level, i can choose Pivot Mode (same as "Insert" as you mentioned). When Point snapping is on it's showing me little dotties on my Sphere's surface, which i can snap the pivot to.
i only found this: http://www.sidefx.com/index.php?option=com_forum&Itemid=172&page=viewtopic&p=86344&sid=4690b3b606a7110b0958e302cd8a2827
