In this work, we propose a method for monitoring and management of rotator-cuff tendon strains in human-robot collaborative physical therapy for rotator cuff rehabilitation. The proposed approach integrates a complex offline biomechanical model with a collaborative, industrial robot arm and an impedance controller. The model is used for computing rotator-cuff tendon strain as a function of human shoulder configuration, muscle activation and external forces. This subject- and injury-specific data is stored in \textit{strain maps}, which represent the relationship between the strains and shoulder DoFs. In our previous work, we implemented strain maps to preplan minimal strain, safe trajectories using two shoulder DoFs, and used the corresponding robot-mediated movement for passive trajectory following for healthy subjects. This work expands on that by implementing two novel functionalities: 1) patient-led movement, and 2) adding the third shoulder DoF and the corresponding control complexities, while still controlling for safe rotator-cuff tendon strains. For patient-led movement, we precomputed unsafe zones for each strain map by clustering and fitting ellipses to the clusters. These unsafe areas with increased risk of (re-)injury are then used to set the impedance control parameters and reference pose for real-time biomechanical safety control. By linearly interpolating between strain maps, smooth and safe movement of the third shoulder DoF is added. The resulting robot control torques guide the patient away from unsafe, high strain shoulder poses in real-time during patient-led movement. The proposed method has the potential to improve the safety, Range of Motion, and muscle activity that the patients receive through robot-mediated physical therapy. The main advantage of this approach is that the patient is free to use and explore their full shoulder RoM, while the robot controls and manages biomechanical safety in real-time. To validate the proposed method, we performed two experiments showcasing two novel functionalities, and a third experiment as proof-of-concept displaying the full method.