In this paper, we propose an approach for ensuring the safety of a vehicle throughout a parking task, even when the vehicle is being operated at varying levels of automation. We start by specifying a vehicle parking task using linear temporal logic formulae that can be model checked for feasibility. The model-checking is facilitated by the construction of a temporal logic tree via Hamilton-Jacobi reachability analysis. Once we know the parking task is feasible for our vehicle model, we utilize the constructed temporal logic tree to directly synthesize control sets. Our approach synthesizes control sets that are least-restrictive in the context of the specification, since they permit any control inputs that are guaranteed not to violate the specification. This least-restrictive characteristic allows for the application of our approach to vehicles under different modes of operation (e.g., human-in-the-loop shared autonomy or fully-automated schemes). Implementing in both simulation and on hardware, we demonstrate the approach's potential for ensuring the safety of vehicles throughout parking tasks, whether they are operated by humans or automated driving systems.