This study presents a novel reset-dominant synaptic weight programming strategy for passive memristor crossbar arrays, enabling high-precision neuromorphic computing without external current compliance circuitry. We introduce a naturally formed Overshoot Suppression Layer (OSL) within a Pt/Al/TiOx/Al2O3/Pt device stack, which intrinsically limits overshoot current during the set process and allows for stable analog switching. Combined with a half-bias programming scheme, this structure significantly suppresses cell-to-cell interference, a critical challenge in high-density memristor arrays. To further enhance weight accuracy, we propose the InitialLow Resistance State (LRS) scheme, a reset-dominant programming method that minimizes abrupt conductance variation induced by set pulses. Using an incremental step pulse with verification algorithm (ISPVA), we successfully programmed 20 discrete conductance levels with a mean vector-matrix multiplication (VMM) error of 419.8 nA. Notably, 99 % of the weights fell within a 1.5 mu A error margin, demonstrating the high precision of our approach. System-level validation was conducted through hardware-based inference using a spiking neural network (SNN) trained on the MNIST dataset, achieving a classification accuracy of 88.85 %, only 1.7 % below the ideal software baseline. This work highlights a scalable and CMOS-compatible solution for achieving accurate, energy-efficient VMM in passive memristor arrays, offering strong potential for next-generation neuromorphic hardware.