Not as complicated as you might think: I attached a string to the pitcher and looped it around the handle of the box out of sight on the other side so that I could adjust the angle. The pitcher kept slipping sideways, so I stuck a piece of tape underneath on the other side so it couldn't be seen. Voila! Cup was propped up from behind by a small lens case so that liquid (iced tea) would tilt toward the camera.
Thanks to everyone for so many nice comments and votes!