While shared autonomy offers significant potential for assistive robotics, key questions remain about how to effectively map 2D control inputs to 6D robot motions. An intuitive framework should allow users to input commands effortlessly, with the robot responding as expected, without users needing to anticipate the impact of their inputs. In this article, we propose a dynamic input mapping framework that links joystick movements to motions on control frames defined along a trajectory encoded with canal surfaces. We evaluate our method in a user study with 20 participants, demonstrating that our input mapping framework reduces the workload and improves usability compared to a baseline mapping with similar motion encoding. To prepare for deployment in assistive scenarios, we built on the development from the accessible gaming community to select an accessible control interface. We then tested the system in an exploratory study, where three wheelchair users controlled the robot for both daily living activities and a creative painting task, demonstrating its feasibility for users closer to our target population.