Assistive robots offer agency to humans with severe motor impairments. Often, these users control high-DoF robots through low-dimensional interfaces, such as using a 1-D sip-and-puff interface to operate a 6-DoF robotic arm. This mismatch results in having access to only a subset of control dimensions at a given time, imposing unintended and artificial constraints on robot motion. As a result, interface-limited demonstrations embed suboptimal motions that reflect interface restrictions rather than user intent. To address this, we present a trajectory reconstruction algorithm that reasons about task, environment, and interface constraints to lift demonstrations into the robot's full control space. We evaluate our approach using real-world demonstrations of ADL-inspired tasks performed via a 2-D joystick and 1-D sip-and-puff control interface, teleoperating two distinct 7-DoF robotic arms. Analyses of the reconstructed demonstrations and derived control policies show that lifted trajectories are faster and more efficient than their interface-constrained counterparts while respecting user preferences.