For a simplified version of my problem, I would like to calculate the bounding box of a layout-transformed (possibly even render-transformed) shape, so that I can always fit
You will get good results with VisualTreeHelper.GetDescendantBounds() and you can use VisualTreeHelper.GetParent() to gain access to the otherwise protected VisualParent property. However what you probably want to do is call GetDescendantBounds on the shape itself, not its parent, because in spite of its name, the method returns the bounds of the parent and all of its decendants.