Hanging EX3 upside-down for overhead shot

We need to shoot a chef cutting vegetables in his kitchen from directly overhead. There is a rail system for lights in the kitchen and little trolleys with rods and pantographs (foba.ch/pdf/FOBA_ceiling_rail_system.pdf) used to hang lights that weight more than the Sony EX3, so we want to use this.

Short of making some L-bracket from scratch, is there an existing device or tripod part to screw the camera on and then screw the device to the rod?

Thanks for any help!