Logic locking techniques have been proposed to protect chip designs from malicious reverse engineering and overproduction. Stripped functionality logic locking (SFLL) has gained substantial traction as a current state of the art method, exhibiting strong resilience against a wide variety of attacks. However, secure instances of SFLL-based locking tend to have high power and area overheads, particularly in its restore units. This work presents a novel architectural approach to restore unit configuration for SFLL-like logic locking methods that treats restore units as an overhead-constrained shareable resource. We describe how resource contention caused by sharing of restore units imposes constraints on the underlying locking scheme from a graph theoretic perspective and propose both a 0-1 ILP and a heuristic clustering algorithm for finding resource-constrained shared locking configurations that satisfy these constraints. We evaluate our sharing method on SFLL-flex and find that our ILP and heuristic methods were each able to achieve a 55% and 31% reduction in power used by locked datapaths synthesized from MediaBench benchmarks while maintaining the same security and functionality compared to datapaths locked with conventional gate-level techniques.