Modal parameter identification for plate reverbs remains a challenging problem in virtual-analog audio effect emulation. Though neural network-based black-box approaches achieve high modeling accuracy, they generally lack interpretability and do not provide access to physically meaningful modal parameters. In this work, we present our solution to Task B of the DAFx Plate Reverb Parameter Estimation Challenge. Our method first estimates the total number of modes and then employs a Matrix Pencil (MP)-guided eigenvalue initialization strategy for a diagonal complex-valued State Space Model (SSM), which can be interpreted as a bank of parallel second-order all-pole filters. Exploiting the linearity of the resulting system, we compute the state impulse responses and replace gradient-based optimization with a closed-form least-squares estimation of the modal gains. The proposed approach enables accurate recovery of the modal parameters while maintaining an interpretable system representation.