We consider the nonprehensile object transportation task known as the waiter's problem, in which a robot must move an object balanced on a tray from one location to another. In contrast to prior works on the robotic waiter's problem, which make the robot tilt a tray rigidly held by its end effector (EE), we use a tray suspended from the EE by ropes, such that it behaves like a three-dimensional pendulum. Some prior works have actuated the robot so that the EE simulates the behavior of a pendulum, because pendular motion reduces the shear forces acting on the transported objects, minimizing the sliding of rigid objects and sloshing in containers of liquid. In contrast, our use of a real hanging tray allows us to obtain the benefits of pendular motion while only actuating a 3 degree-of-freedom (DOF) mobile base, rather than requiring a full 6-DOF manipulator arm. Our experiments in simulation and on real hardware show that the hanging tray substantially reduces both sliding and sloshing compared to a static, rigidly-grasped tray. Furthermore, we integrate the hanging tray into an interactive robot waiter demonstration, which uses computer vision to identify people with a raised hand and visual servoing to steer toward them and allow them to access the tray.