Suggest that you go with a rigging scheme rather than a morph. Not least because a morph will move the vertices in a straight line whereas a joint will be able to rotate them.

Group everything that will move as one piece into the same group.

You'll probably find the hierarchy method easier than using the set up room.

Turn bending off for each part.

All you'll need to do in the joint editor is to set the rotation points.

I appreciate that the above is only a brief outline but I hope it will help to clarify your thoughts.