The cheese method that works for me is to grab a backpack, bag, or other portable container. Head to the plinth and drop said container next to the plinth. Open the container so you see the little inventory box. Grab the idol and stuff it in the container in one move. Close and pick up the container. Casually stroll away whistling innocently. Druids won't react at all. Works even if they're doing the ritual. They'll carry on like it is still there.
