Dragging an item into a ListView object, I receive a ClassCastException at line
156 of ListViewDragSupport.

A look into the drop() method code, reveals what might be the source of that:    

140: public void drop (DropTargetDropEvent dtde) {
...
142:        int index = list.locationToIndex(dtde.getLocation());

*** NodeListModel.getElementAt() returns a VisualizerNode ***
143:        Object obj = list.getModel().getElementAt(index);
...

*** This line tries to cast a VisualizerNode into a Node. ***
*** => ClassCastException ****
156:        PasteType pt =
            DragDropUtilities.getDropType ((Node)obj,
                ExplorerDnDManager.getDefault ().getDraggedTransferable
((DnDConstants.ACTION_MOVE & dropAction) != 0), dropAction);