Superconductor electronics have increasingly shifted away from RSFQ and its variants toward logic families that eliminate explicit gate-level clocking. While this transition enables simpler circuits and more efficient architectures, it also introduces an implicit reliance on dual-rail codes, resulting in inherent gate duplication. This work presents a duplication-aware retiming methodology for Josephson junction (JJ) count minimization, co-optimizing register placement and polarity assignment. The approach applies beyond SFQ to any monotonic circuit. We further identify cell interfaces—specifically, interconnect drivers, receivers, and fanout (FO) elements—as dominant contributors to JJ count in each cell. A new amplifier design is introduced to reduce these costs, integrated within existing SFQ cells, experimentally verified, and characterized to form a new SFQ cell library. Our results demonstrate a 63-71% JJ count reduction in single-cycle implementations and 41-66% reduction in multi-cycle implementations compared to the prior state-of-the-art. The latter establishes a new Pareto frontier, achieving both shorter critical paths and lower JJ counts than the best-to-date single-cycle implementations.