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Memristive devices based on two-dimensional (2D) materials have emerged as potential synaptic candidates for next-generation neuromorphic computing hardware. Here, we introduce a numerical modeling framework that facilitates efficient exploration of the large parameter space for 2D memristive synaptic devices. High-throughput charge-transport simulations are performed to investigate the voltage pulse characteristics for lateral 2D memristors and synaptic device metrics are studied for different weight-update schemes. We show that the same switching mechanism can lead to fundamentally different pulse characteristics influencing not only the device metrics but also the weight-update direction. A thorough analysis of the parameter space allows simultaneous optimization of the linearity, symmetry, and drift in the synaptic behavior that are related through tradeoffs. The presented modeling framework can serve as a tool for designing 2D memristive devices in practical neuromorphic circuits by providing guidelines for materials properties, device functionality, and system performance for target applications.