Bidirectional thrust grants quadrotors a second equilibrium condition and increased control authority, expanding the envelope of possible aggressive maneuvers and enabling inverted flight, perching, and sensing. Prior geometric control approaches extend differential flatness through Hopf fibration-based attitude representations to support bidirectional thrust, but struggle with actuator saturation and motor reversal delay during inversions, requiring heuristic thrust posture scheduling and waypoint tuning. We propose a learning-based framework that modulates a constant reference trajectory to perform compact, position-constrained quadrotor inversions while remaining compatible with traditional trajectory generation and tracking across flight regimes. Separate policies are trained via reinforcement learning for nominal-to-inverted and inverted-to-nominal transitions. In JAX-based simulation, the proposed method achieves the lowest position deviation and settling time across all evaluated baselines, reducing position root mean square error (RMSE) by 32% and settling time by 57% relative to the strongest optimization-based baseline. Hardware experiments demonstrate successful inversion across multiple yaw configurations with position RMSE below 0.35m, and compatibility with downstream trajectory generation and control through circular flight in both regimes. Additionally, we provide an open-source implementation of the proposed framework.