Discrimination between quantum states is a fundamental task in quantum information theory. Given two arbitrary tensor-product quantum states (TPQS), implementing the optimal measurement on the full quantum system may be impractical. Thus, in this work we focus on identifying local measurement schemes that are near-optimal for distinguishing between two general TPQS. We begin by generalizing previous work to show that a locally greedy scheme using Bayesian updating can optimally distinguish between two pure TPQS states. Then, we show the same algorithm has poor performance in distinguishing mixed TPQS, and introduce a modified locally greedy scheme with strictly better performance. In the second part of this work, we compare these simple schemes with a more general dynamic programming (DP) approach that adaptively optimizes over measurement and subsystem ordering in each round.