In this paper we investigate controlling many nonholonomic unicycles that each receive exactly the same inputs. The robots are almost homogeneous, but each robot has a unique parameter that scales its turning rate. Previous work showed that such a collection of robots can be approximately steered to arbitrary Cartesian positions, but not to arbitrary heading angles in a global reference frame. We extend this work by proving we can always steer such a collection of robots exactly to arbitrary range and bearing locations relative to targets in R^2 in a finite number of steps. We also provide existence proofs for controlling the final heading angles of many robots. This work addresses a fundamental challenge in micro- and nanorobotics with possible applications in targeted therapy, sensing, and actuation. Scale hardware experiments validate the control policy. All code is provided online.