Flapping-wing micro-aerial vehicles (FWMAVs) provide unique control challenges both in control authority and in the complexity of modeling flapping-wing aeromechanics. We provide a control-critical, closed-form model for FWMAV flight, particularly tailored to augmenting yaw torque authority of the vehicle (a common challenge for FWMAVs). The model provides invertible nonlinear closed-form expressions for thrust and moments in terms of trigonometric polynomial input voltages and the wingstroke shape, and respects asymmetries inherent to the vehicle. We apply the model to characterize the Harvard RoboBee, providing an optimization-based system identification process. Using the inverted mapping between wingstroke shape and control axes, we achieve lateral and heading control of the vehicle. Our model and asymmetric system identification, in collaboration with the chosen control scheme, allow full control authority of the position and the heading of the vehicle.