Surgical debridement is the process of removing dead or damaged tissue to allow the remaining parts to heal. Automating this procedure could reduce surgical fatigue and facilitate teleoperation, but doing so is challenging for Robotic Surgical Assistants (RSAs) such as the da Vinci Research Kit (dVRK) due to inherent non-linearities in cable-driven systems. Consequently, we propose and evaluate a two-phase calibration process. In Phase I, the robot performs a set of open-loop trajectories to obtain abundant, cheap but coarse data of camera pixels and internal robot joint values, and learns a nonlinear transformation. In Phase II, the robot uses Phase I to move systematically to target points in a printed array. Each time, a human operator manually adjusts the end-effector position by direct contact (not through teleoperation), resulting in a small, high-quality dataset. Experiments suggest that without calibration, position errors are 4.55mm. Phase I alone can reduce average error to 2.14mm, but the combination of Phase I and Phase II reduces average error to 1.08mm. We apply this combination to an approximation of debridement with randomly oriented raisins and pumpkin seeds. Using an endoscopic stereo camera with standard edge detection, experiments with 120 trials achieved success rates of 91.7% to 99.2%, slightly exceeding prior results (89.4%) and more than 2.1x faster, decreasing the time per fragment from 15.8 seconds to 7.3 seconds. Source code, data, and videos are available at https://sites.google.com/view/calib-icra/.